id sid tid token lemma pos 20214 1 1 Transcriber Transcriber NNP 20214 1 2 's 's POS 20214 1 3 Notes note NNS 20214 1 4 ] ] -RRB- 20214 1 5 Conventional conventional JJ 20214 1 6 mathematical mathematical JJ 20214 1 7 notation notation NN 20214 1 8 requires require VBZ 20214 1 9 specialized specialized JJ 20214 1 10 fonts font NNS 20214 1 11 and and CC 20214 1 12 typesetting typesetting NN 20214 1 13 conventions convention NNS 20214 1 14 . . . 20214 2 1 I -PRON- PRP 20214 2 2 have have VBP 20214 2 3 adopted adopt VBN 20214 2 4 modern modern JJ 20214 2 5 computer computer NN 20214 2 6 programming programming NN 20214 2 7 notation notation NN 20214 2 8 using use VBG 20214 2 9 only only JJ 20214 2 10 ASCII ASCII NNP 20214 2 11 characters character NNS 20214 2 12 . . . 20214 3 1 The the DT 20214 3 2 square square JJ 20214 3 3 root root NN 20214 3 4 of of IN 20214 3 5 9 9 CD 20214 3 6 is be VBZ 20214 3 7 thus thus RB 20214 3 8 rendered render VBN 20214 3 9 as as IN 20214 3 10 square_root(9 square_root(9 NNP 20214 3 11 ) ) -RRB- 20214 3 12 and and CC 20214 3 13 the the DT 20214 3 14 square square NN 20214 3 15 of of IN 20214 3 16 9 9 CD 20214 3 17 is be VBZ 20214 3 18 square(9 square(9 JJ 20214 3 19 ) ) -RRB- 20214 3 20 . . . 20214 4 1 10 10 CD 20214 4 2 divided divide VBN 20214 4 3 by by IN 20214 4 4 5 5 CD 20214 4 5 is be VBZ 20214 4 6 ( ( -LRB- 20214 4 7 10/5 10/5 CD 20214 4 8 ) ) -RRB- 20214 4 9 and and CC 20214 4 10 10 10 CD 20214 4 11 multiplied multiply VBN 20214 4 12 by by IN 20214 4 13 5 5 CD 20214 4 14 is be VBZ 20214 4 15 ( ( -LRB- 20214 4 16 10 10 CD 20214 4 17 * * SYM 20214 4 18 5 5 CD 20214 4 19 ) ) -RRB- 20214 4 20 . . . 20214 5 1 The the DT 20214 5 2 DOC DOC NNP 20214 5 3 file file NN 20214 5 4 and and CC 20214 5 5 TXT txt NN 20214 5 6 files file NNS 20214 5 7 otherwise otherwise RB 20214 5 8 closely closely RB 20214 5 9 approximate approximate JJ 20214 5 10 the the DT 20214 5 11 original original JJ 20214 5 12 text text NN 20214 5 13 . . . 20214 6 1 There there EX 20214 6 2 are be VBP 20214 6 3 two two CD 20214 6 4 versions version NNS 20214 6 5 of of IN 20214 6 6 the the DT 20214 6 7 HTML html NN 20214 6 8 files file NNS 20214 6 9 , , , 20214 6 10 one one CD 20214 6 11 closely closely RB 20214 6 12 approximating approximate VBG 20214 6 13 the the DT 20214 6 14 original original JJ 20214 6 15 , , , 20214 6 16 and and CC 20214 6 17 a a DT 20214 6 18 second second JJ 20214 6 19 with with IN 20214 6 20 images image NNS 20214 6 21 of of IN 20214 6 22 the the DT 20214 6 23 slide slide NN 20214 6 24 rule rule NN 20214 6 25 settings setting NNS 20214 6 26 for for IN 20214 6 27 each each DT 20214 6 28 example example NN 20214 6 29 . . . 20214 7 1 By by IN 20214 7 2 the the DT 20214 7 3 time time NN 20214 7 4 I -PRON- PRP 20214 7 5 finished finish VBD 20214 7 6 engineering engineering NN 20214 7 7 school school NN 20214 7 8 in in IN 20214 7 9 1963 1963 CD 20214 7 10 , , , 20214 7 11 the the DT 20214 7 12 slide slide NN 20214 7 13 rule rule NN 20214 7 14 was be VBD 20214 7 15 a a DT 20214 7 16 well well RB 20214 7 17 worn worn JJ 20214 7 18 tool tool NN 20214 7 19 of of IN 20214 7 20 my -PRON- PRP$ 20214 7 21 trade trade NN 20214 7 22 . . . 20214 8 1 I -PRON- PRP 20214 8 2 did do VBD 20214 8 3 not not RB 20214 8 4 use use VB 20214 8 5 an an DT 20214 8 6 electronic electronic JJ 20214 8 7 calculator calculator NN 20214 8 8 for for IN 20214 8 9 another another DT 20214 8 10 ten ten CD 20214 8 11 years year NNS 20214 8 12 . . . 20214 9 1 Consider consider VB 20214 9 2 that that IN 20214 9 3 my -PRON- PRP$ 20214 9 4 predecessors predecessor NNS 20214 9 5 had have VBD 20214 9 6 little little JJ 20214 9 7 else else RB 20214 9 8 to to TO 20214 9 9 use use VB 20214 9 10 -- -- : 20214 9 11 think think VB 20214 9 12 Boulder Boulder NNP 20214 9 13 Dam Dam NNP 20214 9 14 ( ( -LRB- 20214 9 15 with with IN 20214 9 16 all all DT 20214 9 17 its -PRON- PRP$ 20214 9 18 electrical electrical JJ 20214 9 19 , , , 20214 9 20 mechanical mechanical JJ 20214 9 21 and and CC 20214 9 22 construction construction NN 20214 9 23 calculations calculation NNS 20214 9 24 ) ) -RRB- 20214 9 25 . . . 20214 10 1 Rather rather RB 20214 10 2 than than IN 20214 10 3 dealing deal VBG 20214 10 4 with with IN 20214 10 5 elaborate elaborate JJ 20214 10 6 rules rule NNS 20214 10 7 for for IN 20214 10 8 positioning position VBG 20214 10 9 the the DT 20214 10 10 decimal decimal JJ 20214 10 11 point point NN 20214 10 12 , , , 20214 10 13 I -PRON- PRP 20214 10 14 was be VBD 20214 10 15 taught teach VBN 20214 10 16 to to IN 20214 10 17 first first RB 20214 10 18 " " `` 20214 10 19 scale scale NN 20214 10 20 " " '' 20214 10 21 the the DT 20214 10 22 factors factor NNS 20214 10 23 and and CC 20214 10 24 deal deal VBP 20214 10 25 with with IN 20214 10 26 the the DT 20214 10 27 decimal decimal JJ 20214 10 28 position position NN 20214 10 29 separately separately RB 20214 10 30 . . . 20214 11 1 For for IN 20214 11 2 example example NN 20214 11 3 : : : 20214 11 4 1230 1230 CD 20214 11 5 * * NFP 20214 11 6 .000093 .000093 . 20214 11 7 = = NFP 20214 11 8 1.23E3 1.23e3 CD 20214 11 9 * * NFP 20214 11 10 9.3E-5 9.3e-5 CD 20214 11 11 1.23E3 1.23e3 CD 20214 11 12 means mean VBZ 20214 11 13 multiply multiply NNP 20214 11 14 1.23 1.23 CD 20214 11 15 by by IN 20214 11 16 10 10 CD 20214 11 17 to to IN 20214 11 18 the the DT 20214 11 19 power power NN 20214 11 20 3 3 CD 20214 11 21 . . . 20214 12 1 9.3E-5 9.3e-5 CD 20214 12 2 means mean VBZ 20214 12 3 multiply multiply VB 20214 12 4 9.3 9.3 CD 20214 12 5 by by IN 20214 12 6 0.1 0.1 CD 20214 12 7 to to IN 20214 12 8 the the DT 20214 12 9 power power NN 20214 12 10 5 5 CD 20214 12 11 or or CC 20214 12 12 10 10 CD 20214 12 13 to to IN 20214 12 14 the the DT 20214 12 15 power power NN 20214 12 16 -5 -5 NNP 20214 12 17 . . . 20214 13 1 The the DT 20214 13 2 computation computation NN 20214 13 3 is be VBZ 20214 13 4 thus thus RB 20214 13 5 1.23 1.23 CD 20214 13 6 * * NFP 20214 13 7 9.3 9.3 CD 20214 13 8 * * NFP 20214 13 9 1E3 1e3 CD 20214 13 10 * * NFP 20214 13 11 1E-5 1e-5 NN 20214 13 12 The the DT 20214 13 13 exponents exponent NNS 20214 13 14 are be VBP 20214 13 15 simply simply RB 20214 13 16 added add VBN 20214 13 17 . . . 20214 14 1 1.23 1.23 CD 20214 14 2 * * NFP 20214 14 3 9.3 9.3 CD 20214 14 4 * * NFP 20214 14 5 1E-2 1e-2 CD 20214 14 6 = = SYM 20214 14 7 11.4 11.4 CD 20214 14 8 * * NFP 20214 14 9 1E-2 1e-2 CD 20214 14 10 = = SYM 20214 14 11 .114 .114 CD 20214 14 12 When when WRB 20214 14 13 taking take VBG 20214 14 14 roots root NNS 20214 14 15 , , , 20214 14 16 divide divide VB 20214 14 17 the the DT 20214 14 18 exponent exponent NN 20214 14 19 by by IN 20214 14 20 the the DT 20214 14 21 root root NN 20214 14 22 . . . 20214 15 1 The the DT 20214 15 2 square square JJ 20214 15 3 root root NN 20214 15 4 of of IN 20214 15 5 1E6 1e6 CD 20214 15 6 is be VBZ 20214 15 7 1E3 1e3 CD 20214 15 8 The the DT 20214 15 9 cube cube NN 20214 15 10 root root NN 20214 15 11 of of IN 20214 15 12 1E12 1e12 CD 20214 15 13 is be VBZ 20214 15 14 1E4 1e4 CD 20214 15 15 . . . 20214 16 1 When when WRB 20214 16 2 taking take VBG 20214 16 3 powers power NNS 20214 16 4 , , , 20214 16 5 multiply multiply VB 20214 16 6 the the DT 20214 16 7 exponent exponent NN 20214 16 8 by by IN 20214 16 9 the the DT 20214 16 10 power power NN 20214 16 11 . . . 20214 17 1 The the DT 20214 17 2 cube cube NN 20214 17 3 of of IN 20214 17 4 1E5 1e5 CD 20214 17 5 is be VBZ 20214 17 6 1E15 1e15 CD 20214 17 7 . . . 20214 18 1 [ [ -LRB- 20214 18 2 End end NN 20214 18 3 Transcriber Transcriber NNP 20214 18 4 's 's POS 20214 18 5 Notes note NNS 20214 18 6 ] ] -RRB- 20214 18 7 INSTRUCTIONS INSTRUCTIONS NNP 20214 18 8 for for IN 20214 18 9 using use VBG 20214 18 10 a a DT 20214 18 11 SLIDE SLIDE NNP 20214 18 12 RULE rule NN 20214 18 13 SAVE SAVE NNP 20214 18 14 TIME TIME NNP 20214 18 15 ! ! . 20214 19 1 DO do VB 20214 19 2 THE the DT 20214 19 3 FOLLOWING following JJ 20214 19 4 INSTANTLY instantly NN 20214 19 5 WITHOUT without IN 20214 19 6 PAPER paper NN 20214 19 7 AND and CC 20214 19 8 PENCIL PENCIL NNP 20214 19 9 MULTIPLICATION MULTIPLICATION NNP 20214 19 10 DIVISION division NN 20214 19 11 RECIPROCAL RECIPROCAL VBZ 20214 19 12 VALUES values NN 20214 19 13 SQUARES SQUARES NNP 20214 19 14 & & CC 20214 19 15 CUBES CUBES NNP 20214 19 16 EXTRACTION EXTRACTION NNP 20214 19 17 OF of IN 20214 19 18 SQUARE SQUARE NNP 20214 19 19 ROOT ROOT NNS 20214 19 20 EXTRACTION extraction NN 20214 19 21 OF of IN 20214 19 22 CUBE cube NN 20214 19 23 ROOT ROOT NNP 20214 19 24 DIAMETER DIAMETER NNP 20214 19 25 OR or CC 20214 19 26 AREA area NN 20214 19 27 OF of IN 20214 19 28 CIRCLE CIRCLE NNP 20214 19 29 [ [ -LRB- 20214 19 30 Illustration illustration NN 20214 19 31 : : : 20214 19 32 Two two CD 20214 19 33 images image NNS 20214 19 34 of of IN 20214 19 35 a a DT 20214 19 36 slide slide NN 20214 19 37 rule rule NN 20214 19 38 . . . 20214 19 39 ] ] -RRB- 20214 20 1 INSTRUCTIONS INSTRUCTIONS NNP 20214 20 2 FOR for IN 20214 20 3 USING use VBG 20214 20 4 A a DT 20214 20 5 SLIDE SLIDE NNP 20214 20 6 RULE rule NN 20214 20 7 The the DT 20214 20 8 slide slide NN 20214 20 9 rule rule NN 20214 20 10 is be VBZ 20214 20 11 a a DT 20214 20 12 device device NN 20214 20 13 for for IN 20214 20 14 easily easily RB 20214 20 15 and and CC 20214 20 16 quickly quickly RB 20214 20 17 multiplying multiply VBG 20214 20 18 , , , 20214 20 19 dividing divide VBG 20214 20 20 and and CC 20214 20 21 extracting extract VBG 20214 20 22 square square JJ 20214 20 23 root root NN 20214 20 24 and and CC 20214 20 25 cube cube NN 20214 20 26 root root NN 20214 20 27 . . . 20214 21 1 It -PRON- PRP 20214 21 2 will will MD 20214 21 3 also also RB 20214 21 4 perform perform VB 20214 21 5 any any DT 20214 21 6 combination combination NN 20214 21 7 of of IN 20214 21 8 these these DT 20214 21 9 processes process NNS 20214 21 10 . . . 20214 22 1 On on IN 20214 22 2 this this DT 20214 22 3 account account NN 20214 22 4 , , , 20214 22 5 it -PRON- PRP 20214 22 6 is be VBZ 20214 22 7 found find VBN 20214 22 8 extremely extremely RB 20214 22 9 useful useful JJ 20214 22 10 by by IN 20214 22 11 students student NNS 20214 22 12 and and CC 20214 22 13 teachers teacher NNS 20214 22 14 in in IN 20214 22 15 schools school NNS 20214 22 16 and and CC 20214 22 17 colleges college NNS 20214 22 18 , , , 20214 22 19 by by IN 20214 22 20 engineers engineer NNS 20214 22 21 , , , 20214 22 22 architects architect NNS 20214 22 23 , , , 20214 22 24 draftsmen draftsman NNS 20214 22 25 , , , 20214 22 26 surveyors surveyor NNS 20214 22 27 , , , 20214 22 28 chemists chemist NNS 20214 22 29 , , , 20214 22 30 and and CC 20214 22 31 many many JJ 20214 22 32 others other NNS 20214 22 33 . . . 20214 23 1 Accountants accountant NNS 20214 23 2 and and CC 20214 23 3 clerks clerk NNS 20214 23 4 find find VBP 20214 23 5 it -PRON- PRP 20214 23 6 very very RB 20214 23 7 helpful helpful JJ 20214 23 8 when when WRB 20214 23 9 approximate approximate JJ 20214 23 10 calculations calculation NNS 20214 23 11 must must MD 20214 23 12 be be VB 20214 23 13 made make VBN 20214 23 14 rapidly rapidly RB 20214 23 15 . . . 20214 24 1 The the DT 20214 24 2 operation operation NN 20214 24 3 of of IN 20214 24 4 a a DT 20214 24 5 slide slide NN 20214 24 6 rule rule NN 20214 24 7 is be VBZ 20214 24 8 extremely extremely RB 20214 24 9 easy easy JJ 20214 24 10 , , , 20214 24 11 and and CC 20214 24 12 it -PRON- PRP 20214 24 13 is be VBZ 20214 24 14 well well RB 20214 24 15 worth worth JJ 20214 24 16 while while IN 20214 24 17 for for IN 20214 24 18 anyone anyone NN 20214 24 19 who who WP 20214 24 20 is be VBZ 20214 24 21 called call VBN 20214 24 22 upon upon IN 20214 24 23 to to TO 20214 24 24 do do VB 20214 24 25 much much JJ 20214 24 26 numerical numerical JJ 20214 24 27 calculation calculation NN 20214 24 28 to to TO 20214 24 29 learn learn VB 20214 24 30 to to TO 20214 24 31 use use VB 20214 24 32 one one CD 20214 24 33 . . . 20214 25 1 It -PRON- PRP 20214 25 2 is be VBZ 20214 25 3 the the DT 20214 25 4 purpose purpose NN 20214 25 5 of of IN 20214 25 6 this this DT 20214 25 7 manual manual NN 20214 25 8 to to TO 20214 25 9 explain explain VB 20214 25 10 the the DT 20214 25 11 operation operation NN 20214 25 12 in in IN 20214 25 13 such such PDT 20214 25 14 a a DT 20214 25 15 way way NN 20214 25 16 that that WDT 20214 25 17 a a DT 20214 25 18 person person NN 20214 25 19 who who WP 20214 25 20 has have VBZ 20214 25 21 never never RB 20214 25 22 before before RB 20214 25 23 used use VBN 20214 25 24 a a DT 20214 25 25 slide slide NN 20214 25 26 rule rule NN 20214 25 27 may may MD 20214 25 28 teach teach VB 20214 25 29 himself -PRON- PRP 20214 25 30 to to TO 20214 25 31 do do VB 20214 25 32 so so RB 20214 25 33 . . . 20214 26 1 DESCRIPTION description NN 20214 26 2 OF of IN 20214 26 3 SLIDE SLIDE NNS 20214 26 4 RULE rule VB 20214 26 5 The the DT 20214 26 6 slide slide NN 20214 26 7 rule rule NN 20214 26 8 consists consist VBZ 20214 26 9 of of IN 20214 26 10 three three CD 20214 26 11 parts part NNS 20214 26 12 ( ( -LRB- 20214 26 13 see see VB 20214 26 14 figure figure NN 20214 26 15 1 1 CD 20214 26 16 ) ) -RRB- 20214 26 17 . . . 20214 27 1 B b NN 20214 27 2 is be VBZ 20214 27 3 the the DT 20214 27 4 body body NN 20214 27 5 of of IN 20214 27 6 the the DT 20214 27 7 rule rule NN 20214 27 8 and and CC 20214 27 9 carries carry VBZ 20214 27 10 three three CD 20214 27 11 scales scale NNS 20214 27 12 marked mark VBN 20214 27 13 A a NN 20214 27 14 , , , 20214 27 15 D d NN 20214 27 16 and and CC 20214 27 17 K. K. NNP 20214 27 18 S S NNP 20214 27 19 is be VBZ 20214 27 20 the the DT 20214 27 21 slider slider NN 20214 27 22 which which WDT 20214 27 23 moves move VBZ 20214 27 24 relative relative JJ 20214 27 25 to to IN 20214 27 26 the the DT 20214 27 27 body body NN 20214 27 28 and and CC 20214 27 29 also also RB 20214 27 30 carries carry VBZ 20214 27 31 three three CD 20214 27 32 scales scale NNS 20214 27 33 marked mark VBN 20214 27 34 B B NNP 20214 27 35 , , , 20214 27 36 CI CI NNP 20214 27 37 and and CC 20214 27 38 C. C. NNP 20214 27 39 R R NNP 20214 27 40 is be VBZ 20214 27 41 the the DT 20214 27 42 runner runner NN 20214 27 43 or or CC 20214 27 44 indicator indicator NN 20214 27 45 and and CC 20214 27 46 is be VBZ 20214 27 47 marked mark VBN 20214 27 48 in in IN 20214 27 49 the the DT 20214 27 50 center center NN 20214 27 51 with with IN 20214 27 52 a a DT 20214 27 53 hair hair NN 20214 27 54 - - HYPH 20214 27 55 line line NN 20214 27 56 . . . 20214 28 1 The the DT 20214 28 2 scales scale NNS 20214 28 3 A a NN 20214 28 4 and and CC 20214 28 5 B b NN 20214 28 6 are be VBP 20214 28 7 identical identical JJ 20214 28 8 and and CC 20214 28 9 are be VBP 20214 28 10 used use VBN 20214 28 11 in in IN 20214 28 12 problems problem NNS 20214 28 13 involving involve VBG 20214 28 14 square square JJ 20214 28 15 root root NN 20214 28 16 . . . 20214 29 1 Scales Scales NNP 20214 29 2 C C NNP 20214 29 3 and and CC 20214 29 4 D d NN 20214 29 5 are be VBP 20214 29 6 also also RB 20214 29 7 identical identical JJ 20214 29 8 and and CC 20214 29 9 are be VBP 20214 29 10 used use VBN 20214 29 11 for for IN 20214 29 12 multiplication multiplication NN 20214 29 13 and and CC 20214 29 14 division division NN 20214 29 15 . . . 20214 30 1 Scale Scale NNP 20214 30 2 K k NN 20214 30 3 is be VBZ 20214 30 4 for for IN 20214 30 5 finding find VBG 20214 30 6 cube cube NNP 20214 30 7 root root NN 20214 30 8 . . . 20214 31 1 Scale scale NN 20214 31 2 CI CI NNP 20214 31 3 , , , 20214 31 4 or or CC 20214 31 5 C C NNP 20214 31 6 - - HYPH 20214 31 7 inverse inverse NNP 20214 31 8 , , , 20214 31 9 is be VBZ 20214 31 10 like like IN 20214 31 11 scale scale NN 20214 31 12 C c NN 20214 31 13 except except IN 20214 31 14 that that IN 20214 31 15 it -PRON- PRP 20214 31 16 is be VBZ 20214 31 17 laid lay VBN 20214 31 18 off off RP 20214 31 19 from from IN 20214 31 20 right right NN 20214 31 21 to to IN 20214 31 22 left leave VBN 20214 31 23 instead instead RB 20214 31 24 of of IN 20214 31 25 from from IN 20214 31 26 left leave VBN 20214 31 27 to to IN 20214 31 28 right right NN 20214 31 29 . . . 20214 32 1 It -PRON- PRP 20214 32 2 is be VBZ 20214 32 3 useful useful JJ 20214 32 4 in in IN 20214 32 5 problems problem NNS 20214 32 6 involving involve VBG 20214 32 7 reciprocals reciprocal NNS 20214 32 8 . . . 20214 33 1 MULTIPLICATION MULTIPLICATION NNP 20214 33 2 We -PRON- PRP 20214 33 3 will will MD 20214 33 4 start start VB 20214 33 5 with with IN 20214 33 6 a a DT 20214 33 7 very very RB 20214 33 8 simple simple JJ 20214 33 9 example example NN 20214 33 10 : : : 20214 33 11 Example example NN 20214 33 12 1 1 CD 20214 33 13 : : SYM 20214 33 14 2 2 CD 20214 33 15 * * NFP 20214 33 16 3 3 CD 20214 33 17 = = SYM 20214 33 18 6 6 CD 20214 33 19 To to TO 20214 33 20 prove prove VB 20214 33 21 this this DT 20214 33 22 on on IN 20214 33 23 the the DT 20214 33 24 slide slide NN 20214 33 25 rule rule NN 20214 33 26 , , , 20214 33 27 move move VB 20214 33 28 the the DT 20214 33 29 slider slider NN 20214 33 30 so so IN 20214 33 31 that that IN 20214 33 32 the the DT 20214 33 33 1 1 CD 20214 33 34 at at IN 20214 33 35 the the DT 20214 33 36 left left JJ 20214 33 37 - - HYPH 20214 33 38 hand hand NN 20214 33 39 end end NN 20214 33 40 of of IN 20214 33 41 the the DT 20214 33 42 C C NNP 20214 33 43 scale scale NN 20214 33 44 is be VBZ 20214 33 45 directly directly RB 20214 33 46 over over IN 20214 33 47 the the DT 20214 33 48 large large JJ 20214 33 49 2 2 CD 20214 33 50 on on IN 20214 33 51 the the DT 20214 33 52 D d JJ 20214 33 53 scale scale NN 20214 33 54 ( ( -LRB- 20214 33 55 see see VB 20214 33 56 figure figure NN 20214 33 57 1 1 CD 20214 33 58 ) ) -RRB- 20214 33 59 . . . 20214 34 1 Then then RB 20214 34 2 move move VB 20214 34 3 the the DT 20214 34 4 runner runner NN 20214 34 5 till till IN 20214 34 6 the the DT 20214 34 7 hair hair NN 20214 34 8 - - HYPH 20214 34 9 line line NN 20214 34 10 is be VBZ 20214 34 11 over over IN 20214 34 12 3 3 CD 20214 34 13 on on IN 20214 34 14 the the DT 20214 34 15 C C NNP 20214 34 16 scale scale NN 20214 34 17 . . . 20214 35 1 Read read VB 20214 35 2 the the DT 20214 35 3 answer answer NN 20214 35 4 , , , 20214 35 5 6 6 CD 20214 35 6 , , , 20214 35 7 on on IN 20214 35 8 the the DT 20214 35 9 D d JJ 20214 35 10 scale scale NN 20214 35 11 under under IN 20214 35 12 the the DT 20214 35 13 hair hair NN 20214 35 14 - - HYPH 20214 35 15 line line NN 20214 35 16 . . . 20214 36 1 Now now RB 20214 36 2 , , , 20214 36 3 let let VB 20214 36 4 us -PRON- PRP 20214 36 5 consider consider VB 20214 36 6 a a DT 20214 36 7 more more RBR 20214 36 8 complicated complicated JJ 20214 36 9 example example NN 20214 36 10 : : : 20214 36 11 Example example NN 20214 36 12 2 2 CD 20214 36 13 : : : 20214 36 14 2.12 2.12 CD 20214 36 15 * * NFP 20214 36 16 3.16 3.16 CD 20214 36 17 = = SYM 20214 36 18 6.70 6.70 CD 20214 36 19 As as IN 20214 36 20 before before RB 20214 36 21 , , , 20214 36 22 set set VBD 20214 36 23 the the DT 20214 36 24 1 1 CD 20214 36 25 at at IN 20214 36 26 the the DT 20214 36 27 left left JJ 20214 36 28 - - HYPH 20214 36 29 hand hand NN 20214 36 30 end end NN 20214 36 31 of of IN 20214 36 32 the the DT 20214 36 33 C C NNP 20214 36 34 scale scale NN 20214 36 35 , , , 20214 36 36 which which WDT 20214 36 37 we -PRON- PRP 20214 36 38 will will MD 20214 36 39 call call VB 20214 36 40 the the DT 20214 36 41 left left JJ 20214 36 42 - - HYPH 20214 36 43 hand hand NN 20214 36 44 index index NN 20214 36 45 of of IN 20214 36 46 the the DT 20214 36 47 C C NNP 20214 36 48 scale scale NN 20214 36 49 , , , 20214 36 50 over over IN 20214 36 51 2.12 2.12 CD 20214 36 52 on on IN 20214 36 53 the the DT 20214 36 54 D d JJ 20214 36 55 scale scale NN 20214 36 56 ( ( -LRB- 20214 36 57 See see VB 20214 36 58 figure figure NN 20214 36 59 2 2 CD 20214 36 60 ) ) -RRB- 20214 36 61 . . . 20214 37 1 The the DT 20214 37 2 hair hair NN 20214 37 3 - - HYPH 20214 37 4 line line NN 20214 37 5 of of IN 20214 37 6 the the DT 20214 37 7 runner runner NN 20214 37 8 is be VBZ 20214 37 9 now now RB 20214 37 10 placed place VBN 20214 37 11 over over IN 20214 37 12 3.16 3.16 CD 20214 37 13 on on IN 20214 37 14 the the DT 20214 37 15 C C NNP 20214 37 16 scale scale NN 20214 37 17 and and CC 20214 37 18 the the DT 20214 37 19 answer answer NN 20214 37 20 , , , 20214 37 21 6.70 6.70 CD 20214 37 22 , , , 20214 37 23 read read VBD 20214 37 24 on on IN 20214 37 25 the the DT 20214 37 26 D d JJ 20214 37 27 scale scale NN 20214 37 28 . . . 20214 38 1 METHOD METHOD NNP 20214 38 2 OF of IN 20214 38 3 MAKING make VBG 20214 38 4 SETTINGS SETTINGS NNP 20214 38 5 In in IN 20214 38 6 order order NN 20214 38 7 to to TO 20214 38 8 understand understand VB 20214 38 9 just just RB 20214 38 10 why why WRB 20214 38 11 2.12 2.12 CD 20214 38 12 is be VBZ 20214 38 13 set set VBN 20214 38 14 where where WRB 20214 38 15 it -PRON- PRP 20214 38 16 is be VBZ 20214 38 17 ( ( -LRB- 20214 38 18 figure figure NN 20214 38 19 2 2 CD 20214 38 20 ) ) -RRB- 20214 38 21 , , , 20214 38 22 notice notice VB 20214 38 23 that that IN 20214 38 24 the the DT 20214 38 25 interval interval NN 20214 38 26 from from IN 20214 38 27 2 2 CD 20214 38 28 to to IN 20214 38 29 3 3 CD 20214 38 30 is be VBZ 20214 38 31 divided divide VBN 20214 38 32 into into IN 20214 38 33 10 10 CD 20214 38 34 large large JJ 20214 38 35 or or CC 20214 38 36 major major JJ 20214 38 37 divisions division NNS 20214 38 38 , , , 20214 38 39 each each DT 20214 38 40 of of IN 20214 38 41 which which WDT 20214 38 42 is be VBZ 20214 38 43 , , , 20214 38 44 of of IN 20214 38 45 course course NN 20214 38 46 , , , 20214 38 47 equal equal JJ 20214 38 48 to to IN 20214 38 49 one one CD 20214 38 50 - - HYPH 20214 38 51 tenth tenth NN 20214 38 52 ( ( -LRB- 20214 38 53 0.1 0.1 CD 20214 38 54 ) ) -RRB- 20214 38 55 of of IN 20214 38 56 the the DT 20214 38 57 amount amount NN 20214 38 58 represented represent VBN 20214 38 59 by by IN 20214 38 60 the the DT 20214 38 61 whole whole JJ 20214 38 62 interval interval NN 20214 38 63 . . . 20214 39 1 The the DT 20214 39 2 major major JJ 20214 39 3 divisions division NNS 20214 39 4 are be VBP 20214 39 5 in in IN 20214 39 6 turn turn NN 20214 39 7 divided divide VBN 20214 39 8 into into IN 20214 39 9 5 5 CD 20214 39 10 small small JJ 20214 39 11 or or CC 20214 39 12 minor minor JJ 20214 39 13 divisions division NNS 20214 39 14 , , , 20214 39 15 each each DT 20214 39 16 of of IN 20214 39 17 which which WDT 20214 39 18 is be VBZ 20214 39 19 one one CD 20214 39 20 - - HYPH 20214 39 21 fifth fifth NN 20214 39 22 or or CC 20214 39 23 two two CD 20214 39 24 - - HYPH 20214 39 25 tenths tenth NNS 20214 39 26 ( ( -LRB- 20214 39 27 0.2 0.2 CD 20214 39 28 ) ) -RRB- 20214 39 29 of of IN 20214 39 30 the the DT 20214 39 31 major major JJ 20214 39 32 division division NN 20214 39 33 , , , 20214 39 34 that that RB 20214 39 35 is is RB 20214 39 36 0.02 0.02 CD 20214 39 37 of of IN 20214 39 38 the the DT 20214 39 39 whole whole JJ 20214 39 40 interval interval NN 20214 39 41 . . . 20214 40 1 Therefore therefore RB 20214 40 2 , , , 20214 40 3 the the DT 20214 40 4 index index NN 20214 40 5 is be VBZ 20214 40 6 set set VBN 20214 40 7 above above IN 20214 40 8 2 2 CD 20214 40 9 + + SYM 20214 40 10 1 1 CD 20214 40 11 major major JJ 20214 40 12 division division NN 20214 40 13 + + CC 20214 40 14 1 1 CD 20214 40 15 minor minor JJ 20214 40 16 division division NN 20214 40 17 = = SYM 20214 40 18 2 2 CD 20214 40 19 + + CC 20214 40 20 0.1 0.1 CD 20214 40 21 + + SYM 20214 40 22 0.02 0.02 CD 20214 40 23 = = SYM 20214 40 24 2.12 2.12 CD 20214 40 25 . . . 20214 41 1 In in IN 20214 41 2 the the DT 20214 41 3 same same JJ 20214 41 4 way way NN 20214 41 5 we -PRON- PRP 20214 41 6 find find VBP 20214 41 7 3.16 3.16 CD 20214 41 8 on on IN 20214 41 9 the the DT 20214 41 10 C C NNP 20214 41 11 scale scale NN 20214 41 12 . . . 20214 42 1 While while IN 20214 42 2 we -PRON- PRP 20214 42 3 are be VBP 20214 42 4 on on IN 20214 42 5 this this DT 20214 42 6 subject subject NN 20214 42 7 , , , 20214 42 8 notice notice NN 20214 42 9 that that IN 20214 42 10 in in IN 20214 42 11 the the DT 20214 42 12 interval interval NN 20214 42 13 from from IN 20214 42 14 1 1 CD 20214 42 15 to to IN 20214 42 16 2 2 CD 20214 42 17 the the DT 20214 42 18 major major JJ 20214 42 19 divisions division NNS 20214 42 20 are be VBP 20214 42 21 marked mark VBN 20214 42 22 with with IN 20214 42 23 the the DT 20214 42 24 small small JJ 20214 42 25 figures figure NNS 20214 42 26 1 1 CD 20214 42 27 to to IN 20214 42 28 9 9 CD 20214 42 29 and and CC 20214 42 30 the the DT 20214 42 31 minor minor JJ 20214 42 32 divisions division NNS 20214 42 33 are be VBP 20214 42 34 0.1 0.1 CD 20214 42 35 of of IN 20214 42 36 the the DT 20214 42 37 major major JJ 20214 42 38 divisions division NNS 20214 42 39 . . . 20214 43 1 In in IN 20214 43 2 the the DT 20214 43 3 intervals interval NNS 20214 43 4 from from IN 20214 43 5 2 2 CD 20214 43 6 to to IN 20214 43 7 3 3 CD 20214 43 8 and and CC 20214 43 9 3 3 CD 20214 43 10 to to IN 20214 43 11 4 4 CD 20214 43 12 the the DT 20214 43 13 minor minor JJ 20214 43 14 divisions division NNS 20214 43 15 are be VBP 20214 43 16 0.2 0.2 CD 20214 43 17 of of IN 20214 43 18 the the DT 20214 43 19 major major JJ 20214 43 20 divisions division NNS 20214 43 21 , , , 20214 43 22 and and CC 20214 43 23 for for IN 20214 43 24 the the DT 20214 43 25 rest rest NN 20214 43 26 of of IN 20214 43 27 the the DT 20214 43 28 D d NN 20214 43 29 ( ( -LRB- 20214 43 30 or or CC 20214 43 31 C c NN 20214 43 32 ) ) -RRB- 20214 43 33 scale scale NN 20214 43 34 , , , 20214 43 35 the the DT 20214 43 36 minor minor JJ 20214 43 37 divisions division NNS 20214 43 38 are be VBP 20214 43 39 0.5 0.5 CD 20214 43 40 of of IN 20214 43 41 the the DT 20214 43 42 major major JJ 20214 43 43 divisions division NNS 20214 43 44 . . . 20214 44 1 Reading read VBG 20214 44 2 the the DT 20214 44 3 setting setting NN 20214 44 4 from from IN 20214 44 5 a a DT 20214 44 6 slide slide NN 20214 44 7 rule rule NN 20214 44 8 is be VBZ 20214 44 9 very very RB 20214 44 10 much much RB 20214 44 11 like like IN 20214 44 12 reading read VBG 20214 44 13 measurements measurement NNS 20214 44 14 from from IN 20214 44 15 a a DT 20214 44 16 ruler ruler NN 20214 44 17 . . . 20214 45 1 Imagine imagine VB 20214 45 2 that that IN 20214 45 3 the the DT 20214 45 4 divisions division NNS 20214 45 5 between between IN 20214 45 6 2 2 CD 20214 45 7 and and CC 20214 45 8 3 3 CD 20214 45 9 on on IN 20214 45 10 the the DT 20214 45 11 D d JJ 20214 45 12 scale scale NN 20214 45 13 ( ( -LRB- 20214 45 14 figure figure NN 20214 45 15 2 2 CD 20214 45 16 ) ) -RRB- 20214 45 17 are be VBP 20214 45 18 those those DT 20214 45 19 of of IN 20214 45 20 a a DT 20214 45 21 ruler ruler NN 20214 45 22 divided divide VBN 20214 45 23 into into IN 20214 45 24 tenths tenth NNS 20214 45 25 of of IN 20214 45 26 a a DT 20214 45 27 foot foot NN 20214 45 28 , , , 20214 45 29 and and CC 20214 45 30 each each DT 20214 45 31 tenth tenth NN 20214 45 32 of of IN 20214 45 33 a a DT 20214 45 34 foot foot NN 20214 45 35 divided divide VBN 20214 45 36 in in IN 20214 45 37 5 5 CD 20214 45 38 parts part NNS 20214 45 39 0.02 0.02 CD 20214 45 40 of of IN 20214 45 41 a a DT 20214 45 42 foot foot NN 20214 45 43 long long RB 20214 45 44 . . . 20214 46 1 Then then RB 20214 46 2 the the DT 20214 46 3 distance distance NN 20214 46 4 from from IN 20214 46 5 one one CD 20214 46 6 on on IN 20214 46 7 the the DT 20214 46 8 left left JJ 20214 46 9 - - HYPH 20214 46 10 hand hand NN 20214 46 11 end end NN 20214 46 12 of of IN 20214 46 13 the the DT 20214 46 14 D d JJ 20214 46 15 scale scale NN 20214 46 16 ( ( -LRB- 20214 46 17 not not RB 20214 46 18 shown show VBN 20214 46 19 in in IN 20214 46 20 figure figure NN 20214 46 21 2 2 CD 20214 46 22 ) ) -RRB- 20214 46 23 to to IN 20214 46 24 one one CD 20214 46 25 on on IN 20214 46 26 the the DT 20214 46 27 left left JJ 20214 46 28 - - HYPH 20214 46 29 hand hand NN 20214 46 30 end end NN 20214 46 31 of of IN 20214 46 32 the the DT 20214 46 33 C C NNP 20214 46 34 scale scale NN 20214 46 35 would would MD 20214 46 36 he -PRON- PRP 20214 46 37 2.12 2.12 CD 20214 46 38 feet foot NNS 20214 46 39 . . . 20214 47 1 Of of RB 20214 47 2 course course RB 20214 47 3 , , , 20214 47 4 a a DT 20214 47 5 foot foot NN 20214 47 6 rule rule NN 20214 47 7 is be VBZ 20214 47 8 divided divide VBN 20214 47 9 into into IN 20214 47 10 parts part NNS 20214 47 11 of of IN 20214 47 12 uniform uniform JJ 20214 47 13 length length NN 20214 47 14 , , , 20214 47 15 while while IN 20214 47 16 those those DT 20214 47 17 on on IN 20214 47 18 a a DT 20214 47 19 slide slide NN 20214 47 20 rule rule NN 20214 47 21 get get VBP 20214 47 22 smaller small JJR 20214 47 23 toward toward IN 20214 47 24 the the DT 20214 47 25 right right JJ 20214 47 26 - - HYPH 20214 47 27 hand hand NN 20214 47 28 end end NN 20214 47 29 , , , 20214 47 30 but but CC 20214 47 31 this this DT 20214 47 32 example example NN 20214 47 33 may may MD 20214 47 34 help help VB 20214 47 35 to to TO 20214 47 36 give give VB 20214 47 37 an an DT 20214 47 38 idea idea NN 20214 47 39 of of IN 20214 47 40 the the DT 20214 47 41 method method NN 20214 47 42 of of IN 20214 47 43 making make VBG 20214 47 44 and and CC 20214 47 45 reading read VBG 20214 47 46 settings setting NNS 20214 47 47 . . . 20214 48 1 Now now RB 20214 48 2 consider consider VB 20214 48 3 another another DT 20214 48 4 example example NN 20214 48 5 . . . 20214 49 1 Example Example NNP 20214 49 2 3a 3a NNP 20214 49 3 : : : 20214 49 4 2.12 2.12 CD 20214 49 5 * * NFP 20214 49 6 7.35 7.35 CD 20214 49 7 = = SYM 20214 49 8 15.6 15.6 CD 20214 49 9 If if IN 20214 49 10 we -PRON- PRP 20214 49 11 set set VBD 20214 49 12 the the DT 20214 49 13 left left JJ 20214 49 14 - - HYPH 20214 49 15 hand hand NN 20214 49 16 index index NN 20214 49 17 of of IN 20214 49 18 the the DT 20214 49 19 C C NNP 20214 49 20 scale scale NN 20214 49 21 over over IN 20214 49 22 2.12 2.12 CD 20214 49 23 as as IN 20214 49 24 in in IN 20214 49 25 the the DT 20214 49 26 last last JJ 20214 49 27 example example NN 20214 49 28 , , , 20214 49 29 we -PRON- PRP 20214 49 30 find find VBP 20214 49 31 that that IN 20214 49 32 7.35 7.35 CD 20214 49 33 on on IN 20214 49 34 the the DT 20214 49 35 C C NNP 20214 49 36 scale scale NN 20214 49 37 falls fall VBZ 20214 49 38 out out RP 20214 49 39 beyond beyond IN 20214 49 40 the the DT 20214 49 41 body body NN 20214 49 42 of of IN 20214 49 43 the the DT 20214 49 44 rule rule NN 20214 49 45 . . . 20214 50 1 In in IN 20214 50 2 a a DT 20214 50 3 case case NN 20214 50 4 like like IN 20214 50 5 this this DT 20214 50 6 , , , 20214 50 7 simply simply RB 20214 50 8 use use VB 20214 50 9 the the DT 20214 50 10 right right JJ 20214 50 11 - - HYPH 20214 50 12 hand hand NN 20214 50 13 index index NN 20214 50 14 of of IN 20214 50 15 the the DT 20214 50 16 C C NNP 20214 50 17 scale scale NN 20214 50 18 . . . 20214 51 1 If if IN 20214 51 2 we -PRON- PRP 20214 51 3 set set VBP 20214 51 4 this this DT 20214 51 5 over over IN 20214 51 6 2.12 2.12 CD 20214 51 7 on on IN 20214 51 8 the the DT 20214 51 9 D d JJ 20214 51 10 scale scale NN 20214 51 11 and and CC 20214 51 12 move move VB 20214 51 13 the the DT 20214 51 14 runner runner NN 20214 51 15 to to IN 20214 51 16 7.35 7.35 CD 20214 51 17 on on IN 20214 51 18 the the DT 20214 51 19 C C NNP 20214 51 20 scale scale NN 20214 51 21 we -PRON- PRP 20214 51 22 read read VBP 20214 51 23 the the DT 20214 51 24 result result NN 20214 51 25 15.6 15.6 CD 20214 51 26 on on IN 20214 51 27 the the DT 20214 51 28 D d JJ 20214 51 29 scale scale NN 20214 51 30 under under IN 20214 51 31 the the DT 20214 51 32 hair hair NN 20214 51 33 - - HYPH 20214 51 34 line line NN 20214 51 35 . . . 20214 52 1 Now now RB 20214 52 2 , , , 20214 52 3 the the DT 20214 52 4 question question NN 20214 52 5 immediately immediately RB 20214 52 6 arises arise VBZ 20214 52 7 , , , 20214 52 8 why why WRB 20214 52 9 did do VBD 20214 52 10 we -PRON- PRP 20214 52 11 call call VB 20214 52 12 the the DT 20214 52 13 result result NN 20214 52 14 15.6 15.6 CD 20214 52 15 and and CC 20214 52 16 not not RB 20214 52 17 1.56 1.56 CD 20214 52 18 ? ? . 20214 53 1 The the DT 20214 53 2 answer answer NN 20214 53 3 is be VBZ 20214 53 4 that that IN 20214 53 5 the the DT 20214 53 6 slide slide NN 20214 53 7 rule rule NN 20214 53 8 takes take VBZ 20214 53 9 no no DT 20214 53 10 account account NN 20214 53 11 of of IN 20214 53 12 decimal decimal JJ 20214 53 13 points point NNS 20214 53 14 . . . 20214 54 1 Thus thus RB 20214 54 2 , , , 20214 54 3 the the DT 20214 54 4 settings setting NNS 20214 54 5 would would MD 20214 54 6 be be VB 20214 54 7 identical identical JJ 20214 54 8 for for IN 20214 54 9 all all DT 20214 54 10 of of IN 20214 54 11 the the DT 20214 54 12 following follow VBG 20214 54 13 products product NNS 20214 54 14 : : : 20214 54 15 Example example NN 20214 54 16 3 3 CD 20214 54 17 : : : 20214 54 18 a-- a-- CD 20214 54 19 2.12 2.12 CD 20214 54 20 * * NFP 20214 54 21 7.35 7.35 CD 20214 54 22 = = SYM 20214 54 23 15.6 15.6 CD 20214 54 24 b-- b-- NN 20214 54 25 21.2 21.2 CD 20214 54 26 * * NFP 20214 54 27 7.35 7.35 CD 20214 54 28 = = SYM 20214 54 29 156.0 156.0 CD 20214 54 30 c-- c-- VBN 20214 54 31 212 212 CD 20214 54 32 * * NFP 20214 54 33 73.5 73.5 CD 20214 54 34 = = SYM 20214 54 35 15600 15600 CD 20214 54 36 . . . 20214 54 37 d-- d-- NNP 20214 54 38 2.12 2.12 CD 20214 54 39 * * NFP 20214 54 40 .0735 .0735 . 20214 54 41 = = NFP 20214 54 42 .156 .156 CD 20214 54 43 e-- e-- XX 20214 54 44 .00212 .00212 . 20214 54 45 * * NFP 20214 54 46 735 735 CD 20214 54 47 = = NFP 20214 54 48 .0156 .0156 . 20214 54 49 The the DT 20214 54 50 most most RBS 20214 54 51 convenient convenient JJ 20214 54 52 way way NN 20214 54 53 to to TO 20214 54 54 locate locate VB 20214 54 55 the the DT 20214 54 56 decimal decimal JJ 20214 54 57 point point NN 20214 54 58 is be VBZ 20214 54 59 to to TO 20214 54 60 make make VB 20214 54 61 a a DT 20214 54 62 mental mental JJ 20214 54 63 multiplication multiplication NN 20214 54 64 using use VBG 20214 54 65 only only RB 20214 54 66 the the DT 20214 54 67 first first JJ 20214 54 68 digits digit NNS 20214 54 69 in in IN 20214 54 70 the the DT 20214 54 71 given give VBN 20214 54 72 factors factor NNS 20214 54 73 . . . 20214 55 1 Then then RB 20214 55 2 place place VB 20214 55 3 the the DT 20214 55 4 decimal decimal JJ 20214 55 5 point point NN 20214 55 6 in in IN 20214 55 7 the the DT 20214 55 8 slide slide NN 20214 55 9 rule rule NN 20214 55 10 result result VBP 20214 55 11 so so IN 20214 55 12 that that IN 20214 55 13 its -PRON- PRP$ 20214 55 14 value value NN 20214 55 15 is be VBZ 20214 55 16 nearest nearest JJ 20214 55 17 that that DT 20214 55 18 of of IN 20214 55 19 the the DT 20214 55 20 mental mental JJ 20214 55 21 multiplication multiplication NN 20214 55 22 . . . 20214 56 1 Thus thus RB 20214 56 2 , , , 20214 56 3 in in IN 20214 56 4 example example NN 20214 56 5 3a 3a NN 20214 56 6 above above RB 20214 56 7 , , , 20214 56 8 we -PRON- PRP 20214 56 9 can can MD 20214 56 10 multiply multiply VB 20214 56 11 2 2 CD 20214 56 12 by by IN 20214 56 13 7 7 CD 20214 56 14 in in IN 20214 56 15 our -PRON- PRP$ 20214 56 16 heads head NNS 20214 56 17 and and CC 20214 56 18 see see VB 20214 56 19 immediately immediately RB 20214 56 20 that that IN 20214 56 21 the the DT 20214 56 22 decimal decimal JJ 20214 56 23 point point NN 20214 56 24 must must MD 20214 56 25 be be VB 20214 56 26 placed place VBN 20214 56 27 in in IN 20214 56 28 the the DT 20214 56 29 slide slide NN 20214 56 30 rule rule NN 20214 56 31 result result VBP 20214 56 32 156 156 CD 20214 56 33 so so IN 20214 56 34 that that IN 20214 56 35 it -PRON- PRP 20214 56 36 becomes become VBZ 20214 56 37 15.6 15.6 CD 20214 56 38 which which WDT 20214 56 39 is be VBZ 20214 56 40 nearest near JJS 20214 56 41 to to TO 20214 56 42 14 14 CD 20214 56 43 . . . 20214 57 1 In in IN 20214 57 2 example example NN 20214 57 3 3b 3b NN 20214 57 4 ( ( -LRB- 20214 57 5 20 20 CD 20214 57 6 * * SYM 20214 57 7 7 7 CD 20214 57 8 = = SYM 20214 57 9 140 140 CD 20214 57 10 ) ) -RRB- 20214 57 11 , , , 20214 57 12 so so IN 20214 57 13 we -PRON- PRP 20214 57 14 must must MD 20214 57 15 place place VB 20214 57 16 the the DT 20214 57 17 decimal decimal JJ 20214 57 18 point point NN 20214 57 19 to to TO 20214 57 20 give give VB 20214 57 21 156 156 CD 20214 57 22 . . . 20214 58 1 The the DT 20214 58 2 reader reader NN 20214 58 3 can can MD 20214 58 4 readily readily RB 20214 58 5 verify verify VB 20214 58 6 the the DT 20214 58 7 other other JJ 20214 58 8 examples example NNS 20214 58 9 in in IN 20214 58 10 the the DT 20214 58 11 same same JJ 20214 58 12 way way NN 20214 58 13 . . . 20214 59 1 Since since IN 20214 59 2 the the DT 20214 59 3 product product NN 20214 59 4 of of IN 20214 59 5 a a DT 20214 59 6 number number NN 20214 59 7 by by IN 20214 59 8 a a DT 20214 59 9 second second JJ 20214 59 10 number number NN 20214 59 11 is be VBZ 20214 59 12 the the DT 20214 59 13 same same JJ 20214 59 14 as as IN 20214 59 15 the the DT 20214 59 16 product product NN 20214 59 17 of of IN 20214 59 18 the the DT 20214 59 19 second second JJ 20214 59 20 by by IN 20214 59 21 the the DT 20214 59 22 first first JJ 20214 59 23 , , , 20214 59 24 it -PRON- PRP 20214 59 25 makes make VBZ 20214 59 26 no no DT 20214 59 27 difference difference NN 20214 59 28 which which WDT 20214 59 29 of of IN 20214 59 30 the the DT 20214 59 31 two two CD 20214 59 32 numbers number NNS 20214 59 33 is be VBZ 20214 59 34 set set VBN 20214 59 35 first first RB 20214 59 36 on on IN 20214 59 37 the the DT 20214 59 38 slide slide NN 20214 59 39 rule rule NN 20214 59 40 . . . 20214 60 1 Thus thus RB 20214 60 2 , , , 20214 60 3 an an DT 20214 60 4 alternative alternative JJ 20214 60 5 way way NN 20214 60 6 of of IN 20214 60 7 working work VBG 20214 60 8 example example NN 20214 60 9 2 2 CD 20214 60 10 would would MD 20214 60 11 be be VB 20214 60 12 to to TO 20214 60 13 set set VB 20214 60 14 the the DT 20214 60 15 left left JJ 20214 60 16 - - HYPH 20214 60 17 hand hand NN 20214 60 18 index index NN 20214 60 19 of of IN 20214 60 20 the the DT 20214 60 21 C C NNP 20214 60 22 scale scale NN 20214 60 23 over over IN 20214 60 24 3.16 3.16 CD 20214 60 25 on on IN 20214 60 26 the the DT 20214 60 27 D d JJ 20214 60 28 scale scale NN 20214 60 29 and and CC 20214 60 30 move move VB 20214 60 31 the the DT 20214 60 32 runner runner NN 20214 60 33 to to IN 20214 60 34 2.12 2.12 CD 20214 60 35 on on IN 20214 60 36 the the DT 20214 60 37 C C NNP 20214 60 38 scale scale NN 20214 60 39 and and CC 20214 60 40 read read VB 20214 60 41 the the DT 20214 60 42 answer answer NN 20214 60 43 under under IN 20214 60 44 the the DT 20214 60 45 hair hair NN 20214 60 46 - - HYPH 20214 60 47 line line NN 20214 60 48 on on IN 20214 60 49 the the DT 20214 60 50 D d JJ 20214 60 51 scale scale NN 20214 60 52 . . . 20214 61 1 The the DT 20214 61 2 A a NN 20214 61 3 and and CC 20214 61 4 B b NN 20214 61 5 scales scale NNS 20214 61 6 are be VBP 20214 61 7 made make VBN 20214 61 8 up up RP 20214 61 9 of of IN 20214 61 10 two two CD 20214 61 11 identical identical JJ 20214 61 12 halves half NNS 20214 61 13 each each DT 20214 61 14 of of IN 20214 61 15 which which WDT 20214 61 16 is be VBZ 20214 61 17 very very RB 20214 61 18 similar similar JJ 20214 61 19 to to IN 20214 61 20 the the DT 20214 61 21 C C NNP 20214 61 22 and and CC 20214 61 23 D D NNP 20214 61 24 scales scale NNS 20214 61 25 . . . 20214 62 1 Multiplication Multiplication NNP 20214 62 2 can can MD 20214 62 3 also also RB 20214 62 4 be be VB 20214 62 5 carried carry VBN 20214 62 6 out out RP 20214 62 7 on on IN 20214 62 8 either either CC 20214 62 9 half half NN 20214 62 10 of of IN 20214 62 11 the the DT 20214 62 12 A a NN 20214 62 13 and and CC 20214 62 14 B b NN 20214 62 15 scales scale VBZ 20214 62 16 exactly exactly RB 20214 62 17 as as IN 20214 62 18 it -PRON- PRP 20214 62 19 is be VBZ 20214 62 20 done do VBN 20214 62 21 on on IN 20214 62 22 the the DT 20214 62 23 C c NN 20214 62 24 and and CC 20214 62 25 D D NNP 20214 62 26 scales scale NNS 20214 62 27 . . . 20214 63 1 However however RB 20214 63 2 , , , 20214 63 3 since since IN 20214 63 4 the the DT 20214 63 5 A a NN 20214 63 6 and and CC 20214 63 7 B b NN 20214 63 8 scales scale NNS 20214 63 9 are be VBP 20214 63 10 only only RB 20214 63 11 half half RB 20214 63 12 as as RB 20214 63 13 long long RB 20214 63 14 as as IN 20214 63 15 the the DT 20214 63 16 C C NNP 20214 63 17 and and CC 20214 63 18 D D NNP 20214 63 19 scales scale NNS 20214 63 20 , , , 20214 63 21 the the DT 20214 63 22 accuracy accuracy NN 20214 63 23 is be VBZ 20214 63 24 not not RB 20214 63 25 as as RB 20214 63 26 good good JJ 20214 63 27 . . . 20214 64 1 It -PRON- PRP 20214 64 2 is be VBZ 20214 64 3 sometimes sometimes RB 20214 64 4 convenient convenient JJ 20214 64 5 to to TO 20214 64 6 multiply multiply VB 20214 64 7 on on IN 20214 64 8 the the DT 20214 64 9 A a NN 20214 64 10 and and CC 20214 64 11 B B NNP 20214 64 12 scales scale NNS 20214 64 13 in in IN 20214 64 14 more more RBR 20214 64 15 complicated complicated JJ 20214 64 16 problems problem NNS 20214 64 17 as as IN 20214 64 18 we -PRON- PRP 20214 64 19 shall shall MD 20214 64 20 see see VB 20214 64 21 later later RB 20214 64 22 on on RB 20214 64 23 . . . 20214 65 1 A a DT 20214 65 2 group group NN 20214 65 3 of of IN 20214 65 4 examples example NNS 20214 65 5 follow follow VBP 20214 65 6 which which WDT 20214 65 7 cover cover VBP 20214 65 8 all all PDT 20214 65 9 the the DT 20214 65 10 possible possible JJ 20214 65 11 combination combination NN 20214 65 12 of of IN 20214 65 13 settings setting NNS 20214 65 14 which which WDT 20214 65 15 can can MD 20214 65 16 arise arise VB 20214 65 17 in in IN 20214 65 18 the the DT 20214 65 19 multiplication multiplication NN 20214 65 20 of of IN 20214 65 21 two two CD 20214 65 22 numbers number NNS 20214 65 23 . . . 20214 66 1 Example example NN 20214 66 2 4 4 CD 20214 66 3 : : SYM 20214 66 4 20 20 CD 20214 66 5 * * NFP 20214 66 6 3 3 CD 20214 66 7 = = SYM 20214 66 8 60 60 CD 20214 66 9 5 5 CD 20214 66 10 : : SYM 20214 66 11 85 85 CD 20214 66 12 * * SYM 20214 66 13 2 2 CD 20214 66 14 = = SYM 20214 66 15 170 170 CD 20214 66 16 6 6 CD 20214 66 17 : : : 20214 66 18 45 45 CD 20214 66 19 * * CD 20214 66 20 35 35 CD 20214 66 21 = = SYM 20214 66 22 1575 1575 CD 20214 66 23 7 7 CD 20214 66 24 : : SYM 20214 66 25 151 151 CD 20214 66 26 * * NFP 20214 66 27 42 42 CD 20214 66 28 = = SYM 20214 66 29 6342 6342 CD 20214 66 30 8 8 CD 20214 66 31 : : : 20214 66 32 6.5 6.5 CD 20214 66 33 * * SYM 20214 66 34 15 15 CD 20214 66 35 = = SYM 20214 66 36 97.5 97.5 CD 20214 66 37 9 9 CD 20214 66 38 : : SYM 20214 66 39 .34 .34 NFP 20214 66 40 * * NFP 20214 66 41 .08 .08 NFP 20214 66 42 = = SYM 20214 66 43 .0272 .0272 . 20214 66 44 10 10 CD 20214 66 45 : : : 20214 66 46 75 75 CD 20214 66 47 * * NFP 20214 66 48 26 26 CD 20214 66 49 = = SYM 20214 66 50 1950 1950 CD 20214 66 51 11 11 CD 20214 66 52 : : : 20214 66 53 .00054 .00054 . 20214 66 54 * * NFP 20214 66 55 1.4 1.4 CD 20214 66 56 = = SYM 20214 66 57 .000756 .000756 . 20214 66 58 12 12 CD 20214 66 59 : : SYM 20214 66 60 11.1 11.1 CD 20214 66 61 * * SYM 20214 66 62 2.7 2.7 CD 20214 66 63 = = SYM 20214 66 64 29.97 29.97 CD 20214 66 65 13 13 CD 20214 66 66 : : SYM 20214 66 67 1.01 1.01 CD 20214 66 68 * * NFP 20214 66 69 54 54 CD 20214 66 70 = = SYM 20214 66 71 54.5 54.5 CD 20214 66 72 14 14 CD 20214 66 73 : : : 20214 66 74 3.14 3.14 CD 20214 66 75 * * NFP 20214 66 76 25 25 CD 20214 66 77 = = SYM 20214 66 78 78.5 78.5 CD 20214 66 79 DIVISION DIVISION NNP 20214 66 80 Since since IN 20214 66 81 multiplication multiplication NN 20214 66 82 and and CC 20214 66 83 division division NN 20214 66 84 are be VBP 20214 66 85 inverse inverse NN 20214 66 86 processes process NNS 20214 66 87 , , , 20214 66 88 division division NN 20214 66 89 on on IN 20214 66 90 a a DT 20214 66 91 slide slide NN 20214 66 92 rule rule NN 20214 66 93 is be VBZ 20214 66 94 done do VBN 20214 66 95 by by IN 20214 66 96 making make VBG 20214 66 97 the the DT 20214 66 98 same same JJ 20214 66 99 settings setting NNS 20214 66 100 as as IN 20214 66 101 for for IN 20214 66 102 multiplication multiplication NN 20214 66 103 , , , 20214 66 104 but but CC 20214 66 105 in in IN 20214 66 106 reverse reverse JJ 20214 66 107 order order NN 20214 66 108 . . . 20214 67 1 Suppose suppose VB 20214 67 2 we -PRON- PRP 20214 67 3 have have VBP 20214 67 4 the the DT 20214 67 5 example example NN 20214 67 6 : : : 20214 67 7 Example example NN 20214 67 8 15 15 CD 20214 67 9 : : : 20214 67 10 ( ( -LRB- 20214 67 11 6.70 6.70 CD 20214 67 12 / / SYM 20214 67 13 2.12 2.12 CD 20214 67 14 ) ) -RRB- 20214 67 15 = = SYM 20214 67 16 3.16 3.16 CD 20214 67 17 Set set NN 20214 67 18 indicator indicator NN 20214 67 19 over over IN 20214 67 20 the the DT 20214 67 21 dividend dividend NN 20214 67 22 6.70 6.70 CD 20214 67 23 on on IN 20214 67 24 the the DT 20214 67 25 D d JJ 20214 67 26 scale scale NN 20214 67 27 . . . 20214 68 1 Move move VB 20214 68 2 the the DT 20214 68 3 slider slider NN 20214 68 4 until until IN 20214 68 5 the the DT 20214 68 6 divisor divisor JJ 20214 68 7 2.12 2.12 CD 20214 68 8 on on IN 20214 68 9 the the DT 20214 68 10 C C NNP 20214 68 11 scale scale NN 20214 68 12 is be VBZ 20214 68 13 under under IN 20214 68 14 the the DT 20214 68 15 hair hair NN 20214 68 16 - - HYPH 20214 68 17 line line NN 20214 68 18 . . . 20214 69 1 Then then RB 20214 69 2 read read VB 20214 69 3 the the DT 20214 69 4 result result NN 20214 69 5 on on IN 20214 69 6 the the DT 20214 69 7 D d JJ 20214 69 8 scale scale NN 20214 69 9 under under IN 20214 69 10 the the DT 20214 69 11 left left JJ 20214 69 12 - - HYPH 20214 69 13 hand hand NN 20214 69 14 index index NN 20214 69 15 of of IN 20214 69 16 the the DT 20214 69 17 C C NNP 20214 69 18 scale scale NN 20214 69 19 . . . 20214 70 1 As as IN 20214 70 2 in in IN 20214 70 3 multiplication multiplication NN 20214 70 4 , , , 20214 70 5 the the DT 20214 70 6 decimal decimal JJ 20214 70 7 point point NN 20214 70 8 must must MD 20214 70 9 be be VB 20214 70 10 placed place VBN 20214 70 11 by by IN 20214 70 12 a a DT 20214 70 13 separate separate JJ 20214 70 14 process process NN 20214 70 15 . . . 20214 71 1 Make make VB 20214 71 2 all all PDT 20214 71 3 the the DT 20214 71 4 digits digit NNS 20214 71 5 except except IN 20214 71 6 the the DT 20214 71 7 first first JJ 20214 71 8 in in IN 20214 71 9 both both DT 20214 71 10 dividend dividend NN 20214 71 11 and and CC 20214 71 12 divisor divisor NN 20214 71 13 equal equal JJ 20214 71 14 zero zero CD 20214 71 15 and and CC 20214 71 16 mentally mentally RB 20214 71 17 divide divide VBP 20214 71 18 the the DT 20214 71 19 resulting result VBG 20214 71 20 numbers number NNS 20214 71 21 . . . 20214 72 1 Place place VB 20214 72 2 the the DT 20214 72 3 decimal decimal JJ 20214 72 4 point point NN 20214 72 5 in in IN 20214 72 6 the the DT 20214 72 7 slide slide NN 20214 72 8 rule rule NN 20214 72 9 result result VBP 20214 72 10 so so IN 20214 72 11 that that IN 20214 72 12 it -PRON- PRP 20214 72 13 is be VBZ 20214 72 14 nearest near JJS 20214 72 15 to to IN 20214 72 16 the the DT 20214 72 17 mental mental JJ 20214 72 18 result result NN 20214 72 19 . . . 20214 73 1 In in IN 20214 73 2 example example NN 20214 73 3 15 15 CD 20214 73 4 , , , 20214 73 5 we -PRON- PRP 20214 73 6 mentally mentally RB 20214 73 7 divide divide VBP 20214 73 8 6 6 CD 20214 73 9 by by IN 20214 73 10 2 2 CD 20214 73 11 . . . 20214 74 1 Then then RB 20214 74 2 we -PRON- PRP 20214 74 3 place place VBP 20214 74 4 the the DT 20214 74 5 decimal decimal JJ 20214 74 6 point point NN 20214 74 7 in in IN 20214 74 8 the the DT 20214 74 9 slide slide NN 20214 74 10 rule rule NN 20214 74 11 result result VBP 20214 74 12 316 316 CD 20214 74 13 so so IN 20214 74 14 that that IN 20214 74 15 it -PRON- PRP 20214 74 16 is be VBZ 20214 74 17 3.16 3.16 CD 20214 74 18 which which WDT 20214 74 19 is be VBZ 20214 74 20 nearest near JJS 20214 74 21 to to IN 20214 74 22 3 3 CD 20214 74 23 . . . 20214 75 1 A a DT 20214 75 2 group group NN 20214 75 3 of of IN 20214 75 4 examples example NNS 20214 75 5 for for IN 20214 75 6 practice practice NN 20214 75 7 in in IN 20214 75 8 division division NN 20214 75 9 follow follow NN 20214 75 10 : : : 20214 75 11 Example example NN 20214 75 12 16 16 CD 20214 75 13 : : : 20214 75 14 34 34 CD 20214 75 15 / / SYM 20214 75 16 2 2 CD 20214 75 17 = = SYM 20214 75 18 17 17 CD 20214 75 19 17 17 CD 20214 75 20 : : SYM 20214 75 21 49 49 CD 20214 75 22 / / SYM 20214 75 23 7 7 CD 20214 75 24 = = SYM 20214 75 25 7 7 CD 20214 75 26 18 18 CD 20214 75 27 : : SYM 20214 75 28 132 132 CD 20214 75 29 / / SYM 20214 75 30 12 12 CD 20214 75 31 = = SYM 20214 75 32 11 11 CD 20214 75 33 19 19 CD 20214 75 34 : : : 20214 75 35 480 480 CD 20214 75 36 / / SYM 20214 75 37 16 16 CD 20214 75 38 = = SYM 20214 75 39 30 30 CD 20214 75 40 20 20 CD 20214 75 41 : : SYM 20214 75 42 1.05 1.05 CD 20214 75 43 / / SYM 20214 75 44 35 35 CD 20214 75 45 = = SYM 20214 75 46 .03 .03 CD 20214 75 47 21 21 CD 20214 75 48 : : SYM 20214 75 49 4.32 4.32 CD 20214 75 50 / / SYM 20214 75 51 12 12 CD 20214 75 52 = = SYM 20214 75 53 .36 .36 CD 20214 75 54 22 22 CD 20214 75 55 : : : 20214 75 56 5.23 5.23 CD 20214 75 57 / / SYM 20214 75 58 6.15 6.15 CD 20214 75 59 = = SYM 20214 75 60 .85 .85 CD 20214 75 61 23 23 CD 20214 75 62 : : SYM 20214 75 63 17.1 17.1 CD 20214 75 64 / / SYM 20214 75 65 4.5 4.5 CD 20214 75 66 = = SYM 20214 75 67 3.8 3.8 CD 20214 75 68 24 24 CD 20214 75 69 : : SYM 20214 75 70 1895 1895 CD 20214 75 71 / / SYM 20214 75 72 6.06 6.06 CD 20214 75 73 = = SYM 20214 75 74 313 313 CD 20214 75 75 25 25 CD 20214 75 76 : : : 20214 75 77 45 45 CD 20214 75 78 / / SYM 20214 75 79 .017 .017 CD 20214 75 80 = = SYM 20214 75 81 2647 2647 CD 20214 75 82 THE the DT 20214 75 83 CI CI NNP 20214 75 84 SCALE SCALE NNP 20214 75 85 If if IN 20214 75 86 we -PRON- PRP 20214 75 87 divide divide VBP 20214 75 88 one one CD 20214 75 89 ( ( -LRB- 20214 75 90 1 1 CD 20214 75 91 ) ) -RRB- 20214 75 92 by by IN 20214 75 93 any any DT 20214 75 94 number number NN 20214 75 95 the the DT 20214 75 96 answer answer NN 20214 75 97 is be VBZ 20214 75 98 called call VBN 20214 75 99 the the DT 20214 75 100 reciprocal reciprocal NN 20214 75 101 of of IN 20214 75 102 the the DT 20214 75 103 number number NN 20214 75 104 . . . 20214 76 1 Thus thus RB 20214 76 2 , , , 20214 76 3 one one CD 20214 76 4 - - HYPH 20214 76 5 half half NN 20214 76 6 is be VBZ 20214 76 7 the the DT 20214 76 8 reciprocal reciprocal JJ 20214 76 9 of of IN 20214 76 10 two two CD 20214 76 11 , , , 20214 76 12 one one CD 20214 76 13 - - HYPH 20214 76 14 quarter quarter NN 20214 76 15 is be VBZ 20214 76 16 the the DT 20214 76 17 reciprocal reciprocal NNP 20214 76 18 of of IN 20214 76 19 four four CD 20214 76 20 . . . 20214 77 1 If if IN 20214 77 2 we -PRON- PRP 20214 77 3 take take VBP 20214 77 4 any any DT 20214 77 5 number number NN 20214 77 6 , , , 20214 77 7 say say VB 20214 77 8 14 14 CD 20214 77 9 , , , 20214 77 10 and and CC 20214 77 11 multiply multiply VB 20214 77 12 it -PRON- PRP 20214 77 13 by by IN 20214 77 14 the the DT 20214 77 15 reciprocal reciprocal NN 20214 77 16 of of IN 20214 77 17 another another DT 20214 77 18 number number NN 20214 77 19 , , , 20214 77 20 say say VB 20214 77 21 2 2 CD 20214 77 22 , , , 20214 77 23 we -PRON- PRP 20214 77 24 get get VBP 20214 77 25 : : : 20214 77 26 Example example NN 20214 77 27 26 26 CD 20214 77 28 : : : 20214 77 29 14 14 CD 20214 77 30 * * NFP 20214 77 31 ( ( -LRB- 20214 77 32 1/2 1/2 CD 20214 77 33 ) ) -RRB- 20214 77 34 = = SYM 20214 77 35 7 7 CD 20214 77 36 which which WDT 20214 77 37 is be VBZ 20214 77 38 the the DT 20214 77 39 same same JJ 20214 77 40 as as IN 20214 77 41 14 14 CD 20214 77 42 divided divide VBN 20214 77 43 by by IN 20214 77 44 two two CD 20214 77 45 . . . 20214 78 1 This this DT 20214 78 2 process process NN 20214 78 3 can can MD 20214 78 4 be be VB 20214 78 5 carried carry VBN 20214 78 6 out out RP 20214 78 7 directly directly RB 20214 78 8 on on IN 20214 78 9 the the DT 20214 78 10 slide slide NN 20214 78 11 rule rule NN 20214 78 12 by by IN 20214 78 13 use use NN 20214 78 14 of of IN 20214 78 15 the the DT 20214 78 16 CI CI NNP 20214 78 17 scale scale NN 20214 78 18 . . . 20214 79 1 Numbers number NNS 20214 79 2 on on IN 20214 79 3 the the DT 20214 79 4 CI CI NNP 20214 79 5 scale scale NN 20214 79 6 are be VBP 20214 79 7 reciprocals reciprocal NNS 20214 79 8 of of IN 20214 79 9 those those DT 20214 79 10 on on IN 20214 79 11 the the DT 20214 79 12 C C NNP 20214 79 13 scale scale NN 20214 79 14 . . . 20214 80 1 Thus thus RB 20214 80 2 we -PRON- PRP 20214 80 3 see see VBP 20214 80 4 that that IN 20214 80 5 2 2 CD 20214 80 6 on on IN 20214 80 7 the the DT 20214 80 8 CI CI NNP 20214 80 9 scale scale NN 20214 80 10 comes come VBZ 20214 80 11 directly directly RB 20214 80 12 over over IN 20214 80 13 0.5 0.5 CD 20214 80 14 or or CC 20214 80 15 1/2 1/2 CD 20214 80 16 on on IN 20214 80 17 the the DT 20214 80 18 C C NNP 20214 80 19 scale scale NN 20214 80 20 . . . 20214 81 1 Similarly similarly RB 20214 81 2 4 4 CD 20214 81 3 on on IN 20214 81 4 the the DT 20214 81 5 CI CI NNP 20214 81 6 scale scale NN 20214 81 7 comes come VBZ 20214 81 8 over over IN 20214 81 9 0.25 0.25 CD 20214 81 10 or or CC 20214 81 11 1/4 1/4 CD 20214 81 12 on on IN 20214 81 13 the the DT 20214 81 14 C C NNP 20214 81 15 scale scale NN 20214 81 16 , , , 20214 81 17 and and CC 20214 81 18 so so RB 20214 81 19 on on RB 20214 81 20 . . . 20214 82 1 To to TO 20214 82 2 do do VB 20214 82 3 example example NN 20214 82 4 26 26 CD 20214 82 5 by by IN 20214 82 6 use use NN 20214 82 7 of of IN 20214 82 8 the the DT 20214 82 9 CI CI NNP 20214 82 10 scale scale NN 20214 82 11 , , , 20214 82 12 proceed proceed VBP 20214 82 13 exactly exactly RB 20214 82 14 as as IN 20214 82 15 if if IN 20214 82 16 you -PRON- PRP 20214 82 17 were be VBD 20214 82 18 going go VBG 20214 82 19 to to TO 20214 82 20 multiply multiply VB 20214 82 21 in in IN 20214 82 22 the the DT 20214 82 23 usual usual JJ 20214 82 24 manner manner NN 20214 82 25 except except IN 20214 82 26 that that IN 20214 82 27 you -PRON- PRP 20214 82 28 use use VBP 20214 82 29 the the DT 20214 82 30 CI CI NNP 20214 82 31 scale scale NN 20214 82 32 instead instead RB 20214 82 33 of of IN 20214 82 34 the the DT 20214 82 35 C C NNP 20214 82 36 scale scale NN 20214 82 37 . . . 20214 83 1 First first RB 20214 83 2 set set VB 20214 83 3 the the DT 20214 83 4 left left JJ 20214 83 5 - - HYPH 20214 83 6 hand hand NN 20214 83 7 index index NN 20214 83 8 of of IN 20214 83 9 the the DT 20214 83 10 C C NNP 20214 83 11 scale scale NN 20214 83 12 over over IN 20214 83 13 14 14 CD 20214 83 14 on on IN 20214 83 15 the the DT 20214 83 16 D d JJ 20214 83 17 scale scale NN 20214 83 18 . . . 20214 84 1 Then then RB 20214 84 2 move move VB 20214 84 3 the the DT 20214 84 4 indicator indicator NN 20214 84 5 to to IN 20214 84 6 2 2 CD 20214 84 7 on on IN 20214 84 8 the the DT 20214 84 9 CI CI NNP 20214 84 10 scale scale NN 20214 84 11 . . . 20214 85 1 Read read VB 20214 85 2 the the DT 20214 85 3 result result NN 20214 85 4 , , , 20214 85 5 7 7 CD 20214 85 6 , , , 20214 85 7 on on IN 20214 85 8 the the DT 20214 85 9 D d JJ 20214 85 10 scale scale NN 20214 85 11 under under IN 20214 85 12 the the DT 20214 85 13 hair hair NN 20214 85 14 - - HYPH 20214 85 15 line line NN 20214 85 16 . . . 20214 86 1 This this DT 20214 86 2 is be VBZ 20214 86 3 really really RB 20214 86 4 another another DT 20214 86 5 way way NN 20214 86 6 of of IN 20214 86 7 dividing divide VBG 20214 86 8 . . . 20214 87 1 THE the DT 20214 87 2 READER READER NNP 20214 87 3 IS be VBZ 20214 87 4 ADVISED advise VBN 20214 87 5 TO to IN 20214 87 6 WORK work NN 20214 87 7 EXAMPLES examples NN 20214 87 8 16 16 CD 20214 87 9 TO to TO 20214 87 10 25 25 CD 20214 87 11 OVER OVER NNS 20214 87 12 AGAIN again RB 20214 87 13 BY by IN 20214 87 14 USE use NN 20214 87 15 OF of IN 20214 87 16 THE the DT 20214 87 17 CI CI NNP 20214 87 18 SCALE SCALE NNP 20214 87 19 . . . 20214 88 1 SQUARING SQUARING NNP 20214 88 2 AND and CC 20214 88 3 SQUARE SQUARE NNP 20214 88 4 ROOT ROOT NNP 20214 88 5 If if IN 20214 88 6 we -PRON- PRP 20214 88 7 take take VBP 20214 88 8 a a DT 20214 88 9 number number NN 20214 88 10 and and CC 20214 88 11 multiply multiply VB 20214 88 12 it -PRON- PRP 20214 88 13 by by IN 20214 88 14 itself -PRON- PRP 20214 88 15 we -PRON- PRP 20214 88 16 call call VBP 20214 88 17 the the DT 20214 88 18 result result NN 20214 88 19 the the DT 20214 88 20 square square NN 20214 88 21 of of IN 20214 88 22 the the DT 20214 88 23 number number NN 20214 88 24 . . . 20214 89 1 The the DT 20214 89 2 process process NN 20214 89 3 is be VBZ 20214 89 4 called call VBN 20214 89 5 squaring square VBG 20214 89 6 the the DT 20214 89 7 number number NN 20214 89 8 . . . 20214 90 1 If if IN 20214 90 2 we -PRON- PRP 20214 90 3 find find VBP 20214 90 4 the the DT 20214 90 5 number number NN 20214 90 6 which which WDT 20214 90 7 , , , 20214 90 8 when when WRB 20214 90 9 multiplied multiply VBN 20214 90 10 by by IN 20214 90 11 itself -PRON- PRP 20214 90 12 is be VBZ 20214 90 13 equal equal JJ 20214 90 14 to to IN 20214 90 15 a a DT 20214 90 16 given give VBN 20214 90 17 number number NN 20214 90 18 , , , 20214 90 19 the the DT 20214 90 20 former former JJ 20214 90 21 number number NN 20214 90 22 is be VBZ 20214 90 23 called call VBN 20214 90 24 the the DT 20214 90 25 square square JJ 20214 90 26 root root NN 20214 90 27 of of IN 20214 90 28 the the DT 20214 90 29 given give VBN 20214 90 30 number number NN 20214 90 31 . . . 20214 91 1 The the DT 20214 91 2 process process NN 20214 91 3 is be VBZ 20214 91 4 called call VBN 20214 91 5 extracting extract VBG 20214 91 6 the the DT 20214 91 7 square square JJ 20214 91 8 root root NN 20214 91 9 of of IN 20214 91 10 the the DT 20214 91 11 number number NN 20214 91 12 . . . 20214 92 1 Both both DT 20214 92 2 these these DT 20214 92 3 processes process NNS 20214 92 4 may may MD 20214 92 5 be be VB 20214 92 6 carried carry VBN 20214 92 7 out out RP 20214 92 8 on on IN 20214 92 9 the the DT 20214 92 10 A a NN 20214 92 11 and and CC 20214 92 12 D d JJ 20214 92 13 scales scale NNS 20214 92 14 of of IN 20214 92 15 a a DT 20214 92 16 slide slide NN 20214 92 17 rule rule NN 20214 92 18 . . . 20214 93 1 For for IN 20214 93 2 example example NN 20214 93 3 : : : 20214 93 4 Example example NN 20214 93 5 27 27 CD 20214 93 6 : : SYM 20214 93 7 4 4 CD 20214 93 8 * * SYM 20214 93 9 4 4 CD 20214 93 10 = = SYM 20214 93 11 square square NN 20214 93 12 ( ( -LRB- 20214 93 13 4 4 CD 20214 93 14 ) ) -RRB- 20214 93 15 = = SYM 20214 93 16 16 16 CD 20214 93 17 Set set NN 20214 93 18 indicator indicator NN 20214 93 19 over over IN 20214 93 20 4 4 CD 20214 93 21 on on IN 20214 93 22 D d JJ 20214 93 23 scale scale NN 20214 93 24 . . . 20214 94 1 Read read VB 20214 94 2 16 16 CD 20214 94 3 on on IN 20214 94 4 A a DT 20214 94 5 scale scale NN 20214 94 6 under under IN 20214 94 7 hair hair NN 20214 94 8 - - HYPH 20214 94 9 line line NN 20214 94 10 . . . 20214 95 1 Example example NN 20214 95 2 28 28 CD 20214 95 3 : : : 20214 95 4 square square NN 20214 95 5 ( ( -LRB- 20214 95 6 25.4 25.4 CD 20214 95 7 ) ) -RRB- 20214 95 8 = = NFP 20214 95 9 646.0 646.0 CD 20214 95 10 The the DT 20214 95 11 decimal decimal JJ 20214 95 12 point point NN 20214 95 13 must must MD 20214 95 14 be be VB 20214 95 15 placed place VBN 20214 95 16 by by IN 20214 95 17 mental mental JJ 20214 95 18 survey survey NN 20214 95 19 . . . 20214 96 1 We -PRON- PRP 20214 96 2 know know VBP 20214 96 3 that that IN 20214 96 4 square square NN 20214 96 5 ( ( -LRB- 20214 96 6 25.4 25.4 CD 20214 96 7 ) ) -RRB- 20214 96 8 must must MD 20214 96 9 be be VB 20214 96 10 a a DT 20214 96 11 little little RB 20214 96 12 larger large JJR 20214 96 13 than than IN 20214 96 14 square square NN 20214 96 15 ( ( -LRB- 20214 96 16 25 25 CD 20214 96 17 ) ) -RRB- 20214 96 18 = = NFP 20214 96 19 625 625 CD 20214 96 20 so so IN 20214 96 21 that that IN 20214 96 22 it -PRON- PRP 20214 96 23 must must MD 20214 96 24 be be VB 20214 96 25 646.0 646.0 CD 20214 96 26 . . . 20214 97 1 To to TO 20214 97 2 extract extract VB 20214 97 3 a a DT 20214 97 4 square square JJ 20214 97 5 root root NN 20214 97 6 , , , 20214 97 7 we -PRON- PRP 20214 97 8 set set VBD 20214 97 9 the the DT 20214 97 10 indicator indicator NN 20214 97 11 over over IN 20214 97 12 the the DT 20214 97 13 number number NN 20214 97 14 on on IN 20214 97 15 the the DT 20214 97 16 A a DT 20214 97 17 scale scale NN 20214 97 18 and and CC 20214 97 19 read read VB 20214 97 20 the the DT 20214 97 21 result result NN 20214 97 22 under under IN 20214 97 23 the the DT 20214 97 24 hair hair NN 20214 97 25 - - HYPH 20214 97 26 line line NN 20214 97 27 on on IN 20214 97 28 the the DT 20214 97 29 D d JJ 20214 97 30 scale scale NN 20214 97 31 . . . 20214 98 1 When when WRB 20214 98 2 we -PRON- PRP 20214 98 3 examine examine VBP 20214 98 4 the the DT 20214 98 5 A a DT 20214 98 6 scale scale NN 20214 98 7 we -PRON- PRP 20214 98 8 see see VBP 20214 98 9 that that IN 20214 98 10 there there EX 20214 98 11 are be VBP 20214 98 12 two two CD 20214 98 13 places place NNS 20214 98 14 where where WRB 20214 98 15 any any DT 20214 98 16 given give VBN 20214 98 17 number number NN 20214 98 18 may may MD 20214 98 19 be be VB 20214 98 20 set set VBN 20214 98 21 , , , 20214 98 22 so so IN 20214 98 23 we -PRON- PRP 20214 98 24 must must MD 20214 98 25 have have VB 20214 98 26 some some DT 20214 98 27 way way NN 20214 98 28 of of IN 20214 98 29 deciding decide VBG 20214 98 30 in in IN 20214 98 31 a a DT 20214 98 32 given give VBN 20214 98 33 case case NN 20214 98 34 which which WDT 20214 98 35 half half NN 20214 98 36 of of IN 20214 98 37 the the DT 20214 98 38 A a DT 20214 98 39 scale scale NN 20214 98 40 to to TO 20214 98 41 use use VB 20214 98 42 . . . 20214 99 1 The the DT 20214 99 2 rule rule NN 20214 99 3 is be VBZ 20214 99 4 as as IN 20214 99 5 follows follow VBZ 20214 99 6 : : : 20214 99 7 ( ( -LRB- 20214 99 8 a a LS 20214 99 9 ) ) -RRB- 20214 99 10 If if IN 20214 99 11 the the DT 20214 99 12 number number NN 20214 99 13 is be VBZ 20214 99 14 greater great JJR 20214 99 15 than than IN 20214 99 16 one one CD 20214 99 17 . . . 20214 100 1 For for IN 20214 100 2 an an DT 20214 100 3 odd odd JJ 20214 100 4 number number NN 20214 100 5 of of IN 20214 100 6 digits digit NNS 20214 100 7 to to IN 20214 100 8 the the DT 20214 100 9 left left NN 20214 100 10 of of IN 20214 100 11 the the DT 20214 100 12 decimal decimal JJ 20214 100 13 point point NN 20214 100 14 , , , 20214 100 15 use use VB 20214 100 16 the the DT 20214 100 17 left left JJ 20214 100 18 - - HYPH 20214 100 19 hand hand NN 20214 100 20 half half NN 20214 100 21 of of IN 20214 100 22 the the DT 20214 100 23 A a DT 20214 100 24 scale scale NN 20214 100 25 . . . 20214 101 1 For for IN 20214 101 2 an an DT 20214 101 3 even even JJ 20214 101 4 number number NN 20214 101 5 of of IN 20214 101 6 digits digit NNS 20214 101 7 to to IN 20214 101 8 the the DT 20214 101 9 left left NN 20214 101 10 of of IN 20214 101 11 the the DT 20214 101 12 decimal decimal JJ 20214 101 13 point point NN 20214 101 14 , , , 20214 101 15 use use VB 20214 101 16 the the DT 20214 101 17 right right JJ 20214 101 18 - - HYPH 20214 101 19 hand hand NN 20214 101 20 half half NN 20214 101 21 of of IN 20214 101 22 the the DT 20214 101 23 A a DT 20214 101 24 scale scale NN 20214 101 25 . . . 20214 102 1 ( ( -LRB- 20214 102 2 b b LS 20214 102 3 ) ) -RRB- 20214 102 4 If if IN 20214 102 5 the the DT 20214 102 6 number number NN 20214 102 7 is be VBZ 20214 102 8 less less JJR 20214 102 9 than than IN 20214 102 10 one one CD 20214 102 11 . . . 20214 103 1 For for IN 20214 103 2 an an DT 20214 103 3 odd odd JJ 20214 103 4 number number NN 20214 103 5 of of IN 20214 103 6 zeros zero NNS 20214 103 7 to to IN 20214 103 8 the the DT 20214 103 9 right right NN 20214 103 10 of of IN 20214 103 11 the the DT 20214 103 12 decimal decimal JJ 20214 103 13 point point NN 20214 103 14 before before IN 20214 103 15 the the DT 20214 103 16 first first JJ 20214 103 17 digit digit NN 20214 103 18 not not RB 20214 103 19 a a DT 20214 103 20 zero zero CD 20214 103 21 , , , 20214 103 22 use use VB 20214 103 23 the the DT 20214 103 24 left left JJ 20214 103 25 - - HYPH 20214 103 26 hand hand NN 20214 103 27 half half NN 20214 103 28 of of IN 20214 103 29 the the DT 20214 103 30 A a DT 20214 103 31 scale scale NN 20214 103 32 . . . 20214 104 1 For for IN 20214 104 2 none none NN 20214 104 3 or or CC 20214 104 4 any any DT 20214 104 5 even even JJ 20214 104 6 number number NN 20214 104 7 of of IN 20214 104 8 zeros zero NNS 20214 104 9 to to IN 20214 104 10 the the DT 20214 104 11 right right NN 20214 104 12 of of IN 20214 104 13 the the DT 20214 104 14 decimal decimal JJ 20214 104 15 point point NN 20214 104 16 before before IN 20214 104 17 the the DT 20214 104 18 first first JJ 20214 104 19 digit digit NN 20214 104 20 not not RB 20214 104 21 a a DT 20214 104 22 zero zero CD 20214 104 23 , , , 20214 104 24 use use VB 20214 104 25 the the DT 20214 104 26 right right JJ 20214 104 27 - - HYPH 20214 104 28 hand hand NN 20214 104 29 half half NN 20214 104 30 of of IN 20214 104 31 the the DT 20214 104 32 A a DT 20214 104 33 scale scale NN 20214 104 34 . . . 20214 105 1 Example example NN 20214 105 2 29 29 CD 20214 105 3 : : : 20214 105 4 square_root square_root NNP 20214 105 5 ( ( -LRB- 20214 105 6 157 157 CD 20214 105 7 ) ) -RRB- 20214 105 8 = = NFP 20214 105 9 12.5 12.5 CD 20214 105 10 Since since IN 20214 105 11 we -PRON- PRP 20214 105 12 have have VBP 20214 105 13 an an DT 20214 105 14 odd odd JJ 20214 105 15 number number NN 20214 105 16 of of IN 20214 105 17 digits digits JJ 20214 105 18 set set VBN 20214 105 19 indicator indicator NN 20214 105 20 over over IN 20214 105 21 157 157 CD 20214 105 22 on on IN 20214 105 23 left left JJ 20214 105 24 - - HYPH 20214 105 25 hand hand NN 20214 105 26 half half NN 20214 105 27 of of IN 20214 105 28 A a DT 20214 105 29 scale scale NN 20214 105 30 . . . 20214 106 1 Read read VB 20214 106 2 12.5 12.5 CD 20214 106 3 on on IN 20214 106 4 the the DT 20214 106 5 D d JJ 20214 106 6 scale scale NN 20214 106 7 under under IN 20214 106 8 hair hair NN 20214 106 9 - - HYPH 20214 106 10 line line NN 20214 106 11 . . . 20214 107 1 To to TO 20214 107 2 check check VB 20214 107 3 the the DT 20214 107 4 decimal decimal JJ 20214 107 5 point point NN 20214 107 6 think think VB 20214 107 7 of of IN 20214 107 8 the the DT 20214 107 9 perfect perfect JJ 20214 107 10 square square NN 20214 107 11 nearest near JJS 20214 107 12 to to IN 20214 107 13 157 157 CD 20214 107 14 . . . 20214 108 1 It -PRON- PRP 20214 108 2 is be VBZ 20214 108 3 12 12 CD 20214 108 4 * * SYM 20214 108 5 12 12 CD 20214 108 6 = = SYM 20214 108 7 144 144 CD 20214 108 8 , , , 20214 108 9 so so IN 20214 108 10 that that IN 20214 108 11 square_root(157 square_root(157 NNP 20214 108 12 ) ) -RRB- 20214 108 13 must must MD 20214 108 14 be be VB 20214 108 15 a a DT 20214 108 16 little little JJ 20214 108 17 more more JJR 20214 108 18 than than IN 20214 108 19 12 12 CD 20214 108 20 or or CC 20214 108 21 12.5 12.5 CD 20214 108 22 . . . 20214 109 1 Example example NN 20214 109 2 30 30 CD 20214 109 3 : : : 20214 109 4 square_root square_root NNP 20214 109 5 ( ( -LRB- 20214 109 6 .0037 .0037 NFP 20214 109 7 ) ) -RRB- 20214 109 8 = = NFP 20214 109 9 .0608 .0608 . 20214 109 10 In in IN 20214 109 11 this this DT 20214 109 12 number number NN 20214 109 13 we -PRON- PRP 20214 109 14 have have VBP 20214 109 15 an an DT 20214 109 16 even even JJ 20214 109 17 number number NN 20214 109 18 of of IN 20214 109 19 zeros zero NNS 20214 109 20 to to IN 20214 109 21 the the DT 20214 109 22 right right NN 20214 109 23 of of IN 20214 109 24 the the DT 20214 109 25 decimal decimal JJ 20214 109 26 point point NN 20214 109 27 , , , 20214 109 28 so so IN 20214 109 29 we -PRON- PRP 20214 109 30 must must MD 20214 109 31 set set VB 20214 109 32 the the DT 20214 109 33 indicator indicator NN 20214 109 34 over over IN 20214 109 35 37 37 CD 20214 109 36 on on IN 20214 109 37 the the DT 20214 109 38 right right JJ 20214 109 39 - - HYPH 20214 109 40 hand hand NN 20214 109 41 half half NN 20214 109 42 of of IN 20214 109 43 the the DT 20214 109 44 A a DT 20214 109 45 scale scale NN 20214 109 46 . . . 20214 110 1 Read read VB 20214 110 2 608 608 CD 20214 110 3 under under IN 20214 110 4 the the DT 20214 110 5 hair hair NN 20214 110 6 - - HYPH 20214 110 7 line line NN 20214 110 8 on on IN 20214 110 9 D d JJ 20214 110 10 scale scale NN 20214 110 11 . . . 20214 111 1 To to TO 20214 111 2 place place VB 20214 111 3 the the DT 20214 111 4 decimal decimal JJ 20214 111 5 point point NN 20214 111 6 write write VBP 20214 111 7 : : : 20214 111 8 square_root square_root NNP 20214 111 9 ( ( -LRB- 20214 111 10 .0037 .0037 NFP 20214 111 11 ) ) -RRB- 20214 111 12 = = NFP 20214 111 13 square_root square_root NNP 20214 111 14 ( ( -LRB- 20214 111 15 37/10000 37/10000 CD 20214 111 16 ) ) -RRB- 20214 111 17 = = NFP 20214 111 18 1/100 1/100 CD 20214 111 19 square_root square_root NNP 20214 111 20 ( ( -LRB- 20214 111 21 37 37 CD 20214 111 22 ) ) -RRB- 20214 111 23 The the DT 20214 111 24 nearest near RBS 20214 111 25 perfect perfect JJ 20214 111 26 square square NN 20214 111 27 to to IN 20214 111 28 37 37 CD 20214 111 29 is be VBZ 20214 111 30 6 6 CD 20214 111 31 * * SYM 20214 111 32 6 6 CD 20214 111 33 = = SYM 20214 111 34 36 36 CD 20214 111 35 , , , 20214 111 36 so so CC 20214 111 37 the the DT 20214 111 38 answer answer NN 20214 111 39 should should MD 20214 111 40 be be VB 20214 111 41 a a DT 20214 111 42 little little JJ 20214 111 43 more more JJR 20214 111 44 than than IN 20214 111 45 0.06 0.06 CD 20214 111 46 or or CC 20214 111 47 .0608 .0608 . 20214 111 48 . . . 20214 112 1 All all DT 20214 112 2 of of IN 20214 112 3 what what WP 20214 112 4 has have VBZ 20214 112 5 been be VBN 20214 112 6 said say VBN 20214 112 7 about about IN 20214 112 8 use use NN 20214 112 9 of of IN 20214 112 10 the the DT 20214 112 11 A a NN 20214 112 12 and and CC 20214 112 13 D d JJ 20214 112 14 scales scale NNS 20214 112 15 for for IN 20214 112 16 squaring square VBG 20214 112 17 and and CC 20214 112 18 extracting extract VBG 20214 112 19 square square JJ 20214 112 20 root root NN 20214 112 21 applies apply VBZ 20214 112 22 equally equally RB 20214 112 23 well well RB 20214 112 24 to to IN 20214 112 25 the the DT 20214 112 26 B B NNP 20214 112 27 and and CC 20214 112 28 C C NNP 20214 112 29 scales scale VBZ 20214 112 30 since since IN 20214 112 31 they -PRON- PRP 20214 112 32 are be VBP 20214 112 33 identical identical JJ 20214 112 34 to to IN 20214 112 35 the the DT 20214 112 36 A a NN 20214 112 37 and and CC 20214 112 38 D d JJ 20214 112 39 scales scale NNS 20214 112 40 respectively respectively RB 20214 112 41 . . . 20214 113 1 A a DT 20214 113 2 number number NN 20214 113 3 of of IN 20214 113 4 examples example NNS 20214 113 5 follow follow VBP 20214 113 6 for for IN 20214 113 7 squaring squaring NN 20214 113 8 and and CC 20214 113 9 the the DT 20214 113 10 extraction extraction NN 20214 113 11 of of IN 20214 113 12 square square JJ 20214 113 13 root root NN 20214 113 14 . . . 20214 114 1 Example example NN 20214 114 2 31 31 CD 20214 114 3 : : : 20214 114 4 square square NN 20214 114 5 ( ( -LRB- 20214 114 6 2 2 CD 20214 114 7 ) ) -RRB- 20214 114 8 = = SYM 20214 114 9 4 4 CD 20214 114 10 32 32 CD 20214 114 11 : : : 20214 114 12 square square JJ 20214 114 13 ( ( -LRB- 20214 114 14 15 15 CD 20214 114 15 ) ) -RRB- 20214 114 16 = = SYM 20214 114 17 225 225 CD 20214 114 18 33 33 CD 20214 114 19 : : : 20214 114 20 square square NN 20214 114 21 ( ( -LRB- 20214 114 22 26 26 CD 20214 114 23 ) ) -RRB- 20214 114 24 = = NFP 20214 114 25 676 676 CD 20214 114 26 34 34 CD 20214 114 27 : : : 20214 114 28 square square NN 20214 114 29 ( ( -LRB- 20214 114 30 19.65 19.65 CD 20214 114 31 ) ) -RRB- 20214 114 32 = = NFP 20214 114 33 386 386 CD 20214 114 34 35 35 CD 20214 114 35 : : : 20214 114 36 square_root square_root NNP 20214 114 37 ( ( -LRB- 20214 114 38 64 64 CD 20214 114 39 ) ) -RRB- 20214 114 40 = = SYM 20214 114 41 8 8 CD 20214 114 42 36 36 CD 20214 114 43 : : : 20214 114 44 square_root square_root NNP 20214 114 45 ( ( -LRB- 20214 114 46 6.4 6.4 CD 20214 114 47 ) ) -RRB- 20214 114 48 = = SYM 20214 114 49 2.53 2.53 CD 20214 114 50 37 37 CD 20214 114 51 : : : 20214 114 52 square_root square_root NNP 20214 114 53 ( ( -LRB- 20214 114 54 498 498 CD 20214 114 55 ) ) -RRB- 20214 114 56 = = NFP 20214 114 57 22.5 22.5 CD 20214 114 58 38 38 CD 20214 114 59 : : : 20214 114 60 square_root square_root NNP 20214 114 61 ( ( -LRB- 20214 114 62 2500 2500 CD 20214 114 63 ) ) -RRB- 20214 114 64 = = NFP 20214 114 65 50 50 CD 20214 114 66 39 39 CD 20214 114 67 : : : 20214 114 68 square_root square_root NNP 20214 114 69 ( ( -LRB- 20214 114 70 .16 .16 NFP 20214 114 71 ) ) -RRB- 20214 114 72 = = NFP 20214 114 73 .04 .04 NFP 20214 114 74 40 40 CD 20214 114 75 : : : 20214 114 76 square_root square_root NNP 20214 114 77 ( ( -LRB- 20214 114 78 .03 .03 NFP 20214 114 79 ) ) -RRB- 20214 114 80 = = NFP 20214 114 81 .173 .173 CD 20214 114 82 CUBING CUBING NNP 20214 114 83 AND and CC 20214 114 84 CUBE cube NN 20214 114 85 ROOT ROOT NNS 20214 114 86 If if IN 20214 114 87 we -PRON- PRP 20214 114 88 take take VBP 20214 114 89 a a DT 20214 114 90 number number NN 20214 114 91 and and CC 20214 114 92 multiply multiply VB 20214 114 93 it -PRON- PRP 20214 114 94 by by IN 20214 114 95 itself -PRON- PRP 20214 114 96 , , , 20214 114 97 and and CC 20214 114 98 then then RB 20214 114 99 multiply multiply VB 20214 114 100 the the DT 20214 114 101 result result NN 20214 114 102 by by IN 20214 114 103 the the DT 20214 114 104 original original JJ 20214 114 105 number number NN 20214 114 106 we -PRON- PRP 20214 114 107 get get VBP 20214 114 108 what what WP 20214 114 109 is be VBZ 20214 114 110 called call VBN 20214 114 111 the the DT 20214 114 112 cube cube NNP 20214 114 113 of of IN 20214 114 114 the the DT 20214 114 115 original original JJ 20214 114 116 number number NN 20214 114 117 . . . 20214 115 1 This this DT 20214 115 2 process process NN 20214 115 3 is be VBZ 20214 115 4 called call VBN 20214 115 5 cubing cube VBG 20214 115 6 the the DT 20214 115 7 number number NN 20214 115 8 . . . 20214 116 1 The the DT 20214 116 2 reverse reverse JJ 20214 116 3 process process NN 20214 116 4 of of IN 20214 116 5 finding find VBG 20214 116 6 the the DT 20214 116 7 number number NN 20214 116 8 which which WDT 20214 116 9 , , , 20214 116 10 when when WRB 20214 116 11 multiplied multiply VBN 20214 116 12 by by IN 20214 116 13 itself -PRON- PRP 20214 116 14 and and CC 20214 116 15 then then RB 20214 116 16 by by IN 20214 116 17 itself -PRON- PRP 20214 116 18 again again RB 20214 116 19 , , , 20214 116 20 is be VBZ 20214 116 21 equal equal JJ 20214 116 22 to to IN 20214 116 23 the the DT 20214 116 24 given give VBN 20214 116 25 number number NN 20214 116 26 , , , 20214 116 27 is be VBZ 20214 116 28 called call VBN 20214 116 29 extracting extract VBG 20214 116 30 the the DT 20214 116 31 cube cube NN 20214 116 32 root root NN 20214 116 33 of of IN 20214 116 34 the the DT 20214 116 35 given give VBN 20214 116 36 number number NN 20214 116 37 . . . 20214 117 1 Thus thus RB 20214 117 2 , , , 20214 117 3 since since IN 20214 117 4 5 5 CD 20214 117 5 * * SYM 20214 117 6 5 5 CD 20214 117 7 * * SYM 20214 117 8 5 5 CD 20214 117 9 = = SYM 20214 117 10 125 125 CD 20214 117 11 , , , 20214 117 12 125 125 CD 20214 117 13 is be VBZ 20214 117 14 the the DT 20214 117 15 cube cube NN 20214 117 16 of of IN 20214 117 17 5 5 CD 20214 117 18 and and CC 20214 117 19 5 5 CD 20214 117 20 is be VBZ 20214 117 21 the the DT 20214 117 22 cube cube NNP 20214 117 23 root root NN 20214 117 24 of of IN 20214 117 25 125 125 CD 20214 117 26 . . . 20214 118 1 To to TO 20214 118 2 find find VB 20214 118 3 the the DT 20214 118 4 cube cube NN 20214 118 5 of of IN 20214 118 6 any any DT 20214 118 7 number number NN 20214 118 8 on on IN 20214 118 9 the the DT 20214 118 10 slide slide NN 20214 118 11 rule rule NN 20214 118 12 set set VBD 20214 118 13 the the DT 20214 118 14 indicator indicator NN 20214 118 15 over over IN 20214 118 16 the the DT 20214 118 17 number number NN 20214 118 18 on on IN 20214 118 19 the the DT 20214 118 20 D d JJ 20214 118 21 scale scale NN 20214 118 22 and and CC 20214 118 23 read read VB 20214 118 24 the the DT 20214 118 25 answer answer NN 20214 118 26 on on IN 20214 118 27 the the DT 20214 118 28 K K NNP 20214 118 29 scale scale NN 20214 118 30 under under IN 20214 118 31 the the DT 20214 118 32 hair hair NN 20214 118 33 - - HYPH 20214 118 34 line line NN 20214 118 35 . . . 20214 119 1 To to TO 20214 119 2 find find VB 20214 119 3 the the DT 20214 119 4 cube cube NN 20214 119 5 root root NN 20214 119 6 of of IN 20214 119 7 any any DT 20214 119 8 number number NN 20214 119 9 set set VBD 20214 119 10 the the DT 20214 119 11 indicator indicator NN 20214 119 12 over over IN 20214 119 13 the the DT 20214 119 14 number number NN 20214 119 15 on on IN 20214 119 16 the the DT 20214 119 17 K K NNP 20214 119 18 scale scale NN 20214 119 19 and and CC 20214 119 20 read read VB 20214 119 21 the the DT 20214 119 22 answer answer NN 20214 119 23 on on IN 20214 119 24 the the DT 20214 119 25 D d JJ 20214 119 26 scale scale NN 20214 119 27 under under IN 20214 119 28 the the DT 20214 119 29 hair hair NN 20214 119 30 - - HYPH 20214 119 31 line line NN 20214 119 32 . . . 20214 120 1 Just just RB 20214 120 2 as as IN 20214 120 3 on on IN 20214 120 4 the the DT 20214 120 5 A a DT 20214 120 6 scale scale NN 20214 120 7 , , , 20214 120 8 where where WRB 20214 120 9 there there EX 20214 120 10 were be VBD 20214 120 11 two two CD 20214 120 12 places place NNS 20214 120 13 where where WRB 20214 120 14 you -PRON- PRP 20214 120 15 could could MD 20214 120 16 set set VB 20214 120 17 a a DT 20214 120 18 given give VBN 20214 120 19 number number NN 20214 120 20 , , , 20214 120 21 on on IN 20214 120 22 the the DT 20214 120 23 K K NNP 20214 120 24 scale scale NN 20214 120 25 there there EX 20214 120 26 are be VBP 20214 120 27 three three CD 20214 120 28 places place NNS 20214 120 29 where where WRB 20214 120 30 a a DT 20214 120 31 number number NN 20214 120 32 may may MD 20214 120 33 be be VB 20214 120 34 set set VBN 20214 120 35 . . . 20214 121 1 To to TO 20214 121 2 tell tell VB 20214 121 3 which which WDT 20214 121 4 of of IN 20214 121 5 the the DT 20214 121 6 three three CD 20214 121 7 to to TO 20214 121 8 use use VB 20214 121 9 , , , 20214 121 10 we -PRON- PRP 20214 121 11 must must MD 20214 121 12 make make VB 20214 121 13 use use NN 20214 121 14 of of IN 20214 121 15 the the DT 20214 121 16 following follow VBG 20214 121 17 rule rule NN 20214 121 18 . . . 20214 122 1 ( ( -LRB- 20214 122 2 a a LS 20214 122 3 ) ) -RRB- 20214 122 4 If if IN 20214 122 5 the the DT 20214 122 6 number number NN 20214 122 7 is be VBZ 20214 122 8 greater great JJR 20214 122 9 than than IN 20214 122 10 one one CD 20214 122 11 . . . 20214 123 1 For for IN 20214 123 2 1 1 CD 20214 123 3 , , , 20214 123 4 4 4 CD 20214 123 5 , , , 20214 123 6 7 7 CD 20214 123 7 , , , 20214 123 8 10 10 CD 20214 123 9 , , , 20214 123 10 etc etc FW 20214 123 11 . . FW 20214 123 12 , , , 20214 123 13 digits digit VBZ 20214 123 14 to to IN 20214 123 15 the the DT 20214 123 16 left left NN 20214 123 17 of of IN 20214 123 18 the the DT 20214 123 19 decimal decimal JJ 20214 123 20 point point NN 20214 123 21 , , , 20214 123 22 use use VB 20214 123 23 the the DT 20214 123 24 left left JJ 20214 123 25 - - HYPH 20214 123 26 hand hand NN 20214 123 27 third third NN 20214 123 28 of of IN 20214 123 29 the the DT 20214 123 30 K K NNP 20214 123 31 scale scale NN 20214 123 32 . . . 20214 124 1 For for IN 20214 124 2 2 2 CD 20214 124 3 , , , 20214 124 4 5 5 CD 20214 124 5 , , , 20214 124 6 8 8 CD 20214 124 7 , , , 20214 124 8 11 11 CD 20214 124 9 , , , 20214 124 10 etc etc FW 20214 124 11 . . FW 20214 124 12 , , , 20214 124 13 digits digit VBZ 20214 124 14 to to IN 20214 124 15 the the DT 20214 124 16 left left NN 20214 124 17 of of IN 20214 124 18 the the DT 20214 124 19 decimal decimal JJ 20214 124 20 point point NN 20214 124 21 , , , 20214 124 22 use use VB 20214 124 23 the the DT 20214 124 24 middle middle JJ 20214 124 25 third third JJ 20214 124 26 of of IN 20214 124 27 the the DT 20214 124 28 K K NNP 20214 124 29 scale scale NN 20214 124 30 . . . 20214 125 1 For for IN 20214 125 2 3 3 CD 20214 125 3 , , , 20214 125 4 6 6 CD 20214 125 5 , , , 20214 125 6 9 9 CD 20214 125 7 , , , 20214 125 8 12 12 CD 20214 125 9 , , , 20214 125 10 etc etc FW 20214 125 11 . . FW 20214 125 12 , , , 20214 125 13 digits digit VBZ 20214 125 14 to to IN 20214 125 15 the the DT 20214 125 16 left left NN 20214 125 17 of of IN 20214 125 18 the the DT 20214 125 19 decimal decimal JJ 20214 125 20 point point NN 20214 125 21 use use VBP 20214 125 22 the the DT 20214 125 23 right right JJ 20214 125 24 - - HYPH 20214 125 25 hand hand NN 20214 125 26 third third NN 20214 125 27 of of IN 20214 125 28 the the DT 20214 125 29 K K NNP 20214 125 30 scale scale NN 20214 125 31 . . . 20214 126 1 ( ( -LRB- 20214 126 2 b b LS 20214 126 3 ) ) -RRB- 20214 126 4 If if IN 20214 126 5 the the DT 20214 126 6 number number NN 20214 126 7 is be VBZ 20214 126 8 less less JJR 20214 126 9 than than IN 20214 126 10 one one CD 20214 126 11 . . . 20214 127 1 We -PRON- PRP 20214 127 2 now now RB 20214 127 3 tell tell VBP 20214 127 4 which which WDT 20214 127 5 scale scale NN 20214 127 6 to to TO 20214 127 7 use use NN 20214 127 8 by by IN 20214 127 9 counting count VBG 20214 127 10 the the DT 20214 127 11 number number NN 20214 127 12 of of IN 20214 127 13 zeros zero NNS 20214 127 14 to to IN 20214 127 15 the the DT 20214 127 16 right right NN 20214 127 17 of of IN 20214 127 18 the the DT 20214 127 19 decimal decimal JJ 20214 127 20 point point NN 20214 127 21 before before IN 20214 127 22 the the DT 20214 127 23 first first JJ 20214 127 24 digit digit NN 20214 127 25 not not RB 20214 127 26 zero zero CD 20214 127 27 . . . 20214 128 1 If if IN 20214 128 2 there there EX 20214 128 3 are be VBP 20214 128 4 2 2 CD 20214 128 5 , , , 20214 128 6 5 5 CD 20214 128 7 , , , 20214 128 8 8 8 CD 20214 128 9 , , , 20214 128 10 11 11 CD 20214 128 11 , , , 20214 128 12 etc etc FW 20214 128 13 . . FW 20214 128 14 , , , 20214 128 15 zeros zero NNS 20214 128 16 , , , 20214 128 17 use use VB 20214 128 18 the the DT 20214 128 19 left left JJ 20214 128 20 - - HYPH 20214 128 21 hand hand NN 20214 128 22 third third NN 20214 128 23 of of IN 20214 128 24 the the DT 20214 128 25 K K NNP 20214 128 26 scale scale NN 20214 128 27 . . . 20214 129 1 If if IN 20214 129 2 there there EX 20214 129 3 are be VBP 20214 129 4 1 1 CD 20214 129 5 , , , 20214 129 6 4 4 CD 20214 129 7 , , , 20214 129 8 7 7 CD 20214 129 9 , , , 20214 129 10 10 10 CD 20214 129 11 , , , 20214 129 12 etc etc FW 20214 129 13 . . FW 20214 129 14 , , , 20214 129 15 zeros zero NNS 20214 129 16 , , , 20214 129 17 then then RB 20214 129 18 use use VB 20214 129 19 the the DT 20214 129 20 middle middle JJ 20214 129 21 third third JJ 20214 129 22 of of IN 20214 129 23 the the DT 20214 129 24 K K NNP 20214 129 25 scale scale NN 20214 129 26 . . . 20214 130 1 If if IN 20214 130 2 there there EX 20214 130 3 are be VBP 20214 130 4 no no DT 20214 130 5 zeros zero NNS 20214 130 6 or or CC 20214 130 7 3 3 CD 20214 130 8 , , , 20214 130 9 6 6 CD 20214 130 10 , , , 20214 130 11 9 9 CD 20214 130 12 , , , 20214 130 13 12 12 CD 20214 130 14 , , , 20214 130 15 etc etc FW 20214 130 16 . . FW 20214 130 17 , , , 20214 130 18 zeros zero NNS 20214 130 19 , , , 20214 130 20 then then RB 20214 130 21 use use VB 20214 130 22 the the DT 20214 130 23 right right JJ 20214 130 24 - - HYPH 20214 130 25 hand hand NN 20214 130 26 third third NN 20214 130 27 of of IN 20214 130 28 the the DT 20214 130 29 K K NNP 20214 130 30 scale scale NN 20214 130 31 . . . 20214 131 1 For for IN 20214 131 2 example example NN 20214 131 3 : : : 20214 131 4 Example example NN 20214 131 5 41 41 CD 20214 131 6 : : : 20214 131 7 cube_root cube_root NNP 20214 131 8 ( ( -LRB- 20214 131 9 185 185 CD 20214 131 10 ) ) -RRB- 20214 131 11 = = SYM 20214 131 12 5.70 5.70 CD 20214 131 13 Since since IN 20214 131 14 there there EX 20214 131 15 are be VBP 20214 131 16 3 3 CD 20214 131 17 digits digit NNS 20214 131 18 in in IN 20214 131 19 the the DT 20214 131 20 given give VBN 20214 131 21 number number NN 20214 131 22 , , , 20214 131 23 we -PRON- PRP 20214 131 24 set set VBD 20214 131 25 the the DT 20214 131 26 indicator indicator NN 20214 131 27 on on IN 20214 131 28 185 185 CD 20214 131 29 in in IN 20214 131 30 the the DT 20214 131 31 right right JJ 20214 131 32 - - HYPH 20214 131 33 hand hand NN 20214 131 34 third third NN 20214 131 35 of of IN 20214 131 36 the the DT 20214 131 37 K K NNP 20214 131 38 scale scale NN 20214 131 39 , , , 20214 131 40 and and CC 20214 131 41 read read VBD 20214 131 42 the the DT 20214 131 43 result result NN 20214 131 44 570 570 CD 20214 131 45 on on IN 20214 131 46 the the DT 20214 131 47 D d JJ 20214 131 48 scale scale NN 20214 131 49 . . . 20214 132 1 We -PRON- PRP 20214 132 2 can can MD 20214 132 3 place place VB 20214 132 4 the the DT 20214 132 5 decimal decimal JJ 20214 132 6 point point NN 20214 132 7 by by IN 20214 132 8 thinking think VBG 20214 132 9 of of IN 20214 132 10 the the DT 20214 132 11 nearest near JJS 20214 132 12 perfect perfect JJ 20214 132 13 cube cube NNP 20214 132 14 , , , 20214 132 15 which which WDT 20214 132 16 is be VBZ 20214 132 17 125 125 CD 20214 132 18 . . . 20214 133 1 Therefore therefore RB 20214 133 2 , , , 20214 133 3 the the DT 20214 133 4 decimal decimal JJ 20214 133 5 point point NN 20214 133 6 must must MD 20214 133 7 be be VB 20214 133 8 placed place VBN 20214 133 9 so so IN 20214 133 10 as as IN 20214 133 11 to to TO 20214 133 12 give give VB 20214 133 13 5.70 5.70 CD 20214 133 14 , , , 20214 133 15 which which WDT 20214 133 16 is be VBZ 20214 133 17 nearest near JJS 20214 133 18 to to TO 20214 133 19 5 5 CD 20214 133 20 , , , 20214 133 21 the the DT 20214 133 22 cube cube NNP 20214 133 23 root root NN 20214 133 24 of of IN 20214 133 25 125 125 CD 20214 133 26 . . . 20214 134 1 Example example NN 20214 134 2 42 42 CD 20214 134 3 : : : 20214 134 4 cube_root cube_root NNP 20214 134 5 ( ( -LRB- 20214 134 6 .034 .034 CD 20214 134 7 ) ) -RRB- 20214 134 8 = = NFP 20214 134 9 .324 .324 . 20214 134 10 Since since IN 20214 134 11 there there EX 20214 134 12 is be VBZ 20214 134 13 one one CD 20214 134 14 zero zero CD 20214 134 15 between between IN 20214 134 16 the the DT 20214 134 17 decimal decimal JJ 20214 134 18 point point NN 20214 134 19 and and CC 20214 134 20 the the DT 20214 134 21 first first JJ 20214 134 22 digit digit NN 20214 134 23 not not RB 20214 134 24 zero zero CD 20214 134 25 , , , 20214 134 26 we -PRON- PRP 20214 134 27 must must MD 20214 134 28 set set VB 20214 134 29 the the DT 20214 134 30 indicator indicator NN 20214 134 31 over over IN 20214 134 32 34 34 CD 20214 134 33 on on IN 20214 134 34 the the DT 20214 134 35 middle middle JJ 20214 134 36 third third JJ 20214 134 37 of of IN 20214 134 38 the the DT 20214 134 39 K K NNP 20214 134 40 scale scale NN 20214 134 41 . . . 20214 135 1 We -PRON- PRP 20214 135 2 read read VBP 20214 135 3 the the DT 20214 135 4 result result NN 20214 135 5 324 324 CD 20214 135 6 on on IN 20214 135 7 the the DT 20214 135 8 D d JJ 20214 135 9 scale scale NN 20214 135 10 . . . 20214 136 1 The the DT 20214 136 2 decimal decimal JJ 20214 136 3 point point NN 20214 136 4 may may MD 20214 136 5 be be VB 20214 136 6 placed place VBN 20214 136 7 as as IN 20214 136 8 follows follow VBZ 20214 136 9 : : : 20214 136 10 cube_root cube_root NNP 20214 136 11 ( ( -LRB- 20214 136 12 .034 .034 CD 20214 136 13 ) ) -RRB- 20214 136 14 = = NFP 20214 136 15 cube_root cube_root NNP 20214 136 16 ( ( -LRB- 20214 136 17 34/1000 34/1000 CD 20214 136 18 ) ) -RRB- 20214 136 19 = = SYM 20214 136 20 1/10 1/10 CD 20214 136 21 cube_root cube_root NNP 20214 136 22 ( ( -LRB- 20214 136 23 34 34 CD 20214 136 24 ) ) -RRB- 20214 136 25 The the DT 20214 136 26 nearest near RBS 20214 136 27 perfect perfect JJ 20214 136 28 cube cube NN 20214 136 29 to to IN 20214 136 30 34 34 CD 20214 136 31 is be VBZ 20214 136 32 27 27 CD 20214 136 33 , , , 20214 136 34 so so CC 20214 136 35 our -PRON- PRP$ 20214 136 36 answer answer NN 20214 136 37 must must MD 20214 136 38 be be VB 20214 136 39 close close JJ 20214 136 40 to to IN 20214 136 41 one one CD 20214 136 42 - - HYPH 20214 136 43 tenth tenth NN 20214 136 44 of of IN 20214 136 45 the the DT 20214 136 46 cube cube NNP 20214 136 47 root root NN 20214 136 48 of of IN 20214 136 49 27 27 CD 20214 136 50 or or CC 20214 136 51 nearly nearly RB 20214 136 52 0.3 0.3 CD 20214 136 53 . . . 20214 137 1 Therefore therefore RB 20214 137 2 , , , 20214 137 3 we -PRON- PRP 20214 137 4 must must MD 20214 137 5 place place VB 20214 137 6 the the DT 20214 137 7 decimal decimal JJ 20214 137 8 point point NN 20214 137 9 to to TO 20214 137 10 give give VB 20214 137 11 0.324 0.324 CD 20214 137 12 . . . 20214 138 1 A a DT 20214 138 2 group group NN 20214 138 3 of of IN 20214 138 4 examples example NNS 20214 138 5 for for IN 20214 138 6 practice practice NN 20214 138 7 in in IN 20214 138 8 extraction extraction NN 20214 138 9 of of IN 20214 138 10 cube cube NN 20214 138 11 root root NN 20214 138 12 follows follow VBZ 20214 138 13 : : : 20214 138 14 Example example NN 20214 138 15 43 43 CD 20214 138 16 : : : 20214 138 17 cube_root cube_root NNP 20214 138 18 ( ( -LRB- 20214 138 19 64 64 CD 20214 138 20 ) ) -RRB- 20214 138 21 = = SYM 20214 138 22 4 4 CD 20214 138 23 44 44 CD 20214 138 24 : : : 20214 138 25 cube_root cube_root NNP 20214 138 26 ( ( -LRB- 20214 138 27 8 8 CD 20214 138 28 ) ) -RRB- 20214 138 29 = = SYM 20214 138 30 2 2 CD 20214 138 31 45 45 CD 20214 138 32 : : : 20214 138 33 cube_root cube_root NNP 20214 138 34 ( ( -LRB- 20214 138 35 343 343 CD 20214 138 36 ) ) -RRB- 20214 138 37 = = SYM 20214 138 38 7 7 CD 20214 138 39 46 46 CD 20214 138 40 : : : 20214 138 41 cube_root cube_root NNP 20214 138 42 ( ( -LRB- 20214 138 43 .000715 .000715 NFP 20214 138 44 ) ) -RRB- 20214 138 45 = = NFP 20214 138 46 .0894 .0894 NFP 20214 138 47 47 47 CD 20214 138 48 : : : 20214 138 49 cube_root cube_root NNP 20214 138 50 ( ( -LRB- 20214 138 51 .00715 .00715 NFP 20214 138 52 ) ) -RRB- 20214 138 53 = = NFP 20214 138 54 .193 .193 CD 20214 138 55 48 48 CD 20214 138 56 : : : 20214 138 57 cube_root cube_root NNP 20214 138 58 ( ( -LRB- 20214 138 59 .0715 .0715 NFP 20214 138 60 ) ) -RRB- 20214 138 61 = = NFP 20214 138 62 .415 .415 CD 20214 138 63 49 49 CD 20214 138 64 : : : 20214 138 65 cube_root cube_root NNP 20214 138 66 ( ( -LRB- 20214 138 67 .516 .516 CD 20214 138 68 ) ) -RRB- 20214 138 69 = = NFP 20214 138 70 .803 .803 CD 20214 138 71 50 50 CD 20214 138 72 : : : 20214 138 73 cube_root cube_root NNP 20214 138 74 ( ( -LRB- 20214 138 75 27.8 27.8 CD 20214 138 76 ) ) -RRB- 20214 138 77 = = SYM 20214 138 78 3.03 3.03 CD 20214 138 79 51 51 CD 20214 138 80 : : : 20214 138 81 cube_root cube_root NNP 20214 138 82 ( ( -LRB- 20214 138 83 5.49 5.49 CD 20214 138 84 ) ) -RRB- 20214 138 85 = = SYM 20214 138 86 1.76 1.76 CD 20214 138 87 52 52 CD 20214 138 88 : : : 20214 138 89 cube_root cube_root NNP 20214 138 90 ( ( -LRB- 20214 138 91 87.1 87.1 CD 20214 138 92 ) ) -RRB- 20214 138 93 = = NFP 20214 138 94 4.43 4.43 CD 20214 138 95 THE THE NNP 20214 138 96 1.5 1.5 CD 20214 138 97 AND and CC 20214 138 98 2/3 2/3 CD 20214 138 99 POWER POWER NNS 20214 138 100 If if IN 20214 138 101 the the DT 20214 138 102 indicator indicator NN 20214 138 103 is be VBZ 20214 138 104 set set VBN 20214 138 105 over over IN 20214 138 106 a a DT 20214 138 107 given give VBN 20214 138 108 number number NN 20214 138 109 on on IN 20214 138 110 the the DT 20214 138 111 A a DT 20214 138 112 scale scale NN 20214 138 113 , , , 20214 138 114 the the DT 20214 138 115 number number NN 20214 138 116 under under IN 20214 138 117 the the DT 20214 138 118 hair hair NN 20214 138 119 - - HYPH 20214 138 120 line line NN 20214 138 121 on on IN 20214 138 122 the the DT 20214 138 123 K K NNP 20214 138 124 scale scale NN 20214 138 125 is be VBZ 20214 138 126 the the DT 20214 138 127 1.5 1.5 CD 20214 138 128 power power NN 20214 138 129 of of IN 20214 138 130 the the DT 20214 138 131 given give VBN 20214 138 132 number number NN 20214 138 133 . . . 20214 139 1 If if IN 20214 139 2 the the DT 20214 139 3 indicator indicator NN 20214 139 4 is be VBZ 20214 139 5 set set VBN 20214 139 6 over over IN 20214 139 7 a a DT 20214 139 8 given give VBN 20214 139 9 number number NN 20214 139 10 on on IN 20214 139 11 the the DT 20214 139 12 K K NNP 20214 139 13 scale scale NN 20214 139 14 , , , 20214 139 15 the the DT 20214 139 16 number number NN 20214 139 17 under under IN 20214 139 18 the the DT 20214 139 19 hair hair NN 20214 139 20 - - HYPH 20214 139 21 line line NN 20214 139 22 on on IN 20214 139 23 the the DT 20214 139 24 A a DT 20214 139 25 scale scale NN 20214 139 26 is be VBZ 20214 139 27 the the DT 20214 139 28 2/3 2/3 CD 20214 139 29 power power NN 20214 139 30 of of IN 20214 139 31 the the DT 20214 139 32 given give VBN 20214 139 33 number number NN 20214 139 34 . . . 20214 140 1 COMBINATIONS combination NNS 20214 140 2 OF of IN 20214 140 3 PROCESSES processes NN 20214 140 4 A a DT 20214 140 5 slide slide NN 20214 140 6 rule rule NN 20214 140 7 is be VBZ 20214 140 8 especially especially RB 20214 140 9 useful useful JJ 20214 140 10 where where WRB 20214 140 11 some some DT 20214 140 12 combination combination NN 20214 140 13 of of IN 20214 140 14 processes process NNS 20214 140 15 is be VBZ 20214 140 16 necessary necessary JJ 20214 140 17 , , , 20214 140 18 like like IN 20214 140 19 multiplying multiply VBG 20214 140 20 3 3 CD 20214 140 21 numbers number NNS 20214 140 22 together together RB 20214 140 23 and and CC 20214 140 24 dividing divide VBG 20214 140 25 by by IN 20214 140 26 a a DT 20214 140 27 third third NN 20214 140 28 . . . 20214 141 1 Operations operation NNS 20214 141 2 of of IN 20214 141 3 this this DT 20214 141 4 sort sort NN 20214 141 5 may may MD 20214 141 6 be be VB 20214 141 7 performed perform VBN 20214 141 8 in in IN 20214 141 9 such such PDT 20214 141 10 a a DT 20214 141 11 way way NN 20214 141 12 that that WDT 20214 141 13 the the DT 20214 141 14 final final JJ 20214 141 15 answer answer NN 20214 141 16 is be VBZ 20214 141 17 obtained obtain VBN 20214 141 18 immediately immediately RB 20214 141 19 without without IN 20214 141 20 finding find VBG 20214 141 21 intermediate intermediate JJ 20214 141 22 results result NNS 20214 141 23 . . . 20214 142 1 1 1 LS 20214 142 2 . . . 20214 143 1 Multiplying multiply VBG 20214 143 2 several several JJ 20214 143 3 numbers number NNS 20214 143 4 together together RB 20214 143 5 . . . 20214 144 1 For for IN 20214 144 2 example example NN 20214 144 3 , , , 20214 144 4 suppose suppose VB 20214 144 5 it -PRON- PRP 20214 144 6 is be VBZ 20214 144 7 desired desire VBN 20214 144 8 to to TO 20214 144 9 multiply multiply VB 20214 144 10 4 4 CD 20214 144 11 * * SYM 20214 144 12 8 8 CD 20214 144 13 * * SYM 20214 144 14 6 6 CD 20214 144 15 . . . 20214 145 1 Place place VB 20214 145 2 the the DT 20214 145 3 right right JJ 20214 145 4 - - HYPH 20214 145 5 hand hand NN 20214 145 6 index index NN 20214 145 7 of of IN 20214 145 8 the the DT 20214 145 9 C C NNP 20214 145 10 scale scale NN 20214 145 11 over over IN 20214 145 12 4 4 CD 20214 145 13 on on IN 20214 145 14 the the DT 20214 145 15 D d JJ 20214 145 16 scale scale NN 20214 145 17 and and CC 20214 145 18 set set VBD 20214 145 19 the the DT 20214 145 20 indicator indicator NN 20214 145 21 over over IN 20214 145 22 8 8 CD 20214 145 23 on on IN 20214 145 24 the the DT 20214 145 25 C C NNP 20214 145 26 scale scale NN 20214 145 27 . . . 20214 146 1 Now now RB 20214 146 2 , , , 20214 146 3 leaving leave VBG 20214 146 4 the the DT 20214 146 5 indicator indicator NN 20214 146 6 where where WRB 20214 146 7 it -PRON- PRP 20214 146 8 is be VBZ 20214 146 9 , , , 20214 146 10 move move VB 20214 146 11 the the DT 20214 146 12 slider slider NN 20214 146 13 till till IN 20214 146 14 the the DT 20214 146 15 right right JJ 20214 146 16 - - HYPH 20214 146 17 hand hand NN 20214 146 18 index index NN 20214 146 19 is be VBZ 20214 146 20 under under IN 20214 146 21 the the DT 20214 146 22 hairline hairline NN 20214 146 23 . . . 20214 147 1 Now now RB 20214 147 2 , , , 20214 147 3 leaving leave VBG 20214 147 4 the the DT 20214 147 5 slider slider NN 20214 147 6 where where WRB 20214 147 7 it -PRON- PRP 20214 147 8 is be VBZ 20214 147 9 , , , 20214 147 10 move move VB 20214 147 11 the the DT 20214 147 12 indicator indicator NN 20214 147 13 until until IN 20214 147 14 it -PRON- PRP 20214 147 15 is be VBZ 20214 147 16 over over IN 20214 147 17 6 6 CD 20214 147 18 on on IN 20214 147 19 the the DT 20214 147 20 C C NNP 20214 147 21 scale scale NN 20214 147 22 , , , 20214 147 23 and and CC 20214 147 24 read read VBD 20214 147 25 the the DT 20214 147 26 result result NN 20214 147 27 , , , 20214 147 28 192 192 CD 20214 147 29 , , , 20214 147 30 on on IN 20214 147 31 the the DT 20214 147 32 D d JJ 20214 147 33 scale scale NN 20214 147 34 . . . 20214 148 1 This this DT 20214 148 2 may may MD 20214 148 3 be be VB 20214 148 4 continued continue VBN 20214 148 5 indefinitely indefinitely RB 20214 148 6 , , , 20214 148 7 and and CC 20214 148 8 so so RB 20214 148 9 as as IN 20214 148 10 many many JJ 20214 148 11 numbers number NNS 20214 148 12 as as IN 20214 148 13 desired desire VBN 20214 148 14 may may MD 20214 148 15 be be VB 20214 148 16 multiplied multiply VBN 20214 148 17 together together RB 20214 148 18 . . . 20214 149 1 Example example NN 20214 149 2 53 53 CD 20214 149 3 : : : 20214 149 4 2.32 2.32 CD 20214 149 5 * * NFP 20214 149 6 154 154 CD 20214 149 7 * * NFP 20214 149 8 .0375 .0375 . 20214 149 9 * * NFP 20214 149 10 .56 .56 NFP 20214 149 11 = = SYM 20214 149 12 7.54 7.54 CD 20214 149 13 2 2 CD 20214 149 14 . . . 20214 150 1 Multiplication Multiplication NNP 20214 150 2 and and CC 20214 150 3 division division NN 20214 150 4 . . . 20214 151 1 Suppose suppose VB 20214 151 2 we -PRON- PRP 20214 151 3 wish wish VBP 20214 151 4 to to TO 20214 151 5 do do VB 20214 151 6 the the DT 20214 151 7 following follow VBG 20214 151 8 example example NN 20214 151 9 : : : 20214 151 10 Example example NN 20214 151 11 54 54 CD 20214 151 12 : : : 20214 151 13 ( ( -LRB- 20214 151 14 4 4 CD 20214 151 15 * * SYM 20214 151 16 15 15 CD 20214 151 17 ) ) -RRB- 20214 151 18 / / SYM 20214 151 19 2.5 2.5 CD 20214 151 20 = = SYM 20214 151 21 24 24 CD 20214 151 22 First first JJ 20214 151 23 divide divide NN 20214 151 24 4 4 CD 20214 151 25 by by IN 20214 151 26 2.5 2.5 CD 20214 151 27 . . . 20214 152 1 Set Set VBN 20214 152 2 indicator indicator NN 20214 152 3 over over IN 20214 152 4 4 4 CD 20214 152 5 on on IN 20214 152 6 the the DT 20214 152 7 D d JJ 20214 152 8 scale scale NN 20214 152 9 and and CC 20214 152 10 move move VB 20214 152 11 the the DT 20214 152 12 slider slider NN 20214 152 13 until until IN 20214 152 14 2.5 2.5 CD 20214 152 15 is be VBZ 20214 152 16 under under IN 20214 152 17 the the DT 20214 152 18 hair hair NN 20214 152 19 - - HYPH 20214 152 20 line line NN 20214 152 21 . . . 20214 153 1 The the DT 20214 153 2 result result NN 20214 153 3 of of IN 20214 153 4 this this DT 20214 153 5 division division NN 20214 153 6 , , , 20214 153 7 1.6 1.6 CD 20214 153 8 , , , 20214 153 9 appears appear VBZ 20214 153 10 under under IN 20214 153 11 the the DT 20214 153 12 left left JJ 20214 153 13 - - HYPH 20214 153 14 hand hand NN 20214 153 15 index index NN 20214 153 16 of of IN 20214 153 17 the the DT 20214 153 18 C C NNP 20214 153 19 scale scale NN 20214 153 20 . . . 20214 154 1 We -PRON- PRP 20214 154 2 do do VBP 20214 154 3 not not RB 20214 154 4 need need VB 20214 154 5 to to TO 20214 154 6 write write VB 20214 154 7 it -PRON- PRP 20214 154 8 down down RP 20214 154 9 , , , 20214 154 10 however however RB 20214 154 11 , , , 20214 154 12 but but CC 20214 154 13 we -PRON- PRP 20214 154 14 can can MD 20214 154 15 immediately immediately RB 20214 154 16 move move VB 20214 154 17 the the DT 20214 154 18 indicator indicator NN 20214 154 19 to to IN 20214 154 20 15 15 CD 20214 154 21 on on IN 20214 154 22 the the DT 20214 154 23 C C NNP 20214 154 24 scale scale NN 20214 154 25 and and CC 20214 154 26 read read VBD 20214 154 27 the the DT 20214 154 28 final final JJ 20214 154 29 result result NN 20214 154 30 24 24 CD 20214 154 31 on on IN 20214 154 32 the the DT 20214 154 33 D d JJ 20214 154 34 scale scale NN 20214 154 35 under under IN 20214 154 36 the the DT 20214 154 37 hair hair NN 20214 154 38 - - HYPH 20214 154 39 line line NN 20214 154 40 . . . 20214 155 1 Let let VB 20214 155 2 us -PRON- PRP 20214 155 3 consider consider VB 20214 155 4 a a DT 20214 155 5 more more RBR 20214 155 6 complicated complicated JJ 20214 155 7 problem problem NN 20214 155 8 of of IN 20214 155 9 the the DT 20214 155 10 same same JJ 20214 155 11 type type NN 20214 155 12 : : : 20214 155 13 Example example NN 20214 155 14 55 55 CD 20214 155 15 : : : 20214 155 16 ( ( -LRB- 20214 155 17 30/7.5 30/7.5 NN 20214 155 18 ) ) -RRB- 20214 155 19 * * NFP 20214 155 20 ( ( -LRB- 20214 155 21 2/4 2/4 CD 20214 155 22 ) ) -RRB- 20214 155 23 * * NFP 20214 155 24 ( ( -LRB- 20214 155 25 4.5/5 4.5/5 NN 20214 155 26 ) ) -RRB- 20214 155 27 * * NFP 20214 155 28 ( ( -LRB- 20214 155 29 1.5/3 1.5/3 CD 20214 155 30 ) ) -RRB- 20214 155 31 = = NFP 20214 155 32 .9 .9 . 20214 155 33 First first JJ 20214 155 34 set set VBN 20214 155 35 indicator indicator NN 20214 155 36 over over IN 20214 155 37 30 30 CD 20214 155 38 on on IN 20214 155 39 the the DT 20214 155 40 D d JJ 20214 155 41 scale scale NN 20214 155 42 and and CC 20214 155 43 move move NN 20214 155 44 slider slider NN 20214 155 45 until until IN 20214 155 46 7.5 7.5 CD 20214 155 47 on on IN 20214 155 48 the the DT 20214 155 49 C C NNP 20214 155 50 scale scale NN 20214 155 51 comes come VBZ 20214 155 52 under under IN 20214 155 53 the the DT 20214 155 54 hairline hairline NN 20214 155 55 . . . 20214 156 1 The the DT 20214 156 2 intermediate intermediate JJ 20214 156 3 result result NN 20214 156 4 , , , 20214 156 5 4 4 CD 20214 156 6 , , , 20214 156 7 appears appear VBZ 20214 156 8 under under IN 20214 156 9 the the DT 20214 156 10 right right JJ 20214 156 11 - - HYPH 20214 156 12 hand hand NN 20214 156 13 index index NN 20214 156 14 of of IN 20214 156 15 the the DT 20214 156 16 C C NNP 20214 156 17 scale scale NN 20214 156 18 . . . 20214 157 1 We -PRON- PRP 20214 157 2 do do VBP 20214 157 3 not not RB 20214 157 4 need need VB 20214 157 5 to to TO 20214 157 6 write write VB 20214 157 7 it -PRON- PRP 20214 157 8 down down RP 20214 157 9 but but CC 20214 157 10 merely merely RB 20214 157 11 note note VB 20214 157 12 it -PRON- PRP 20214 157 13 by by IN 20214 157 14 moving move VBG 20214 157 15 the the DT 20214 157 16 indicator indicator NN 20214 157 17 until until IN 20214 157 18 the the DT 20214 157 19 hair hair NN 20214 157 20 - - HYPH 20214 157 21 line line NN 20214 157 22 is be VBZ 20214 157 23 over over IN 20214 157 24 the the DT 20214 157 25 right right JJ 20214 157 26 - - HYPH 20214 157 27 hand hand NN 20214 157 28 index index NN 20214 157 29 of of IN 20214 157 30 the the DT 20214 157 31 C C NNP 20214 157 32 scale scale NN 20214 157 33 . . . 20214 158 1 Now now RB 20214 158 2 we -PRON- PRP 20214 158 3 want want VBP 20214 158 4 to to TO 20214 158 5 multiply multiply VB 20214 158 6 this this DT 20214 158 7 result result NN 20214 158 8 by by IN 20214 158 9 2 2 CD 20214 158 10 , , , 20214 158 11 the the DT 20214 158 12 next next JJ 20214 158 13 factor factor NN 20214 158 14 in in IN 20214 158 15 the the DT 20214 158 16 numerator numerator NN 20214 158 17 . . . 20214 159 1 Since since IN 20214 159 2 two two CD 20214 159 3 is be VBZ 20214 159 4 out out RB 20214 159 5 beyond beyond IN 20214 159 6 the the DT 20214 159 7 body body NN 20214 159 8 of of IN 20214 159 9 the the DT 20214 159 10 rule rule NN 20214 159 11 , , , 20214 159 12 transfer transfer VB 20214 159 13 the the DT 20214 159 14 slider slider NN 20214 159 15 till till IN 20214 159 16 the the DT 20214 159 17 other other JJ 20214 159 18 ( ( -LRB- 20214 159 19 left left JJ 20214 159 20 - - HYPH 20214 159 21 hand hand NN 20214 159 22 ) ) -RRB- 20214 159 23 index index NN 20214 159 24 of of IN 20214 159 25 the the DT 20214 159 26 C C NNP 20214 159 27 scale scale NN 20214 159 28 is be VBZ 20214 159 29 under under IN 20214 159 30 the the DT 20214 159 31 hair hair NN 20214 159 32 - - HYPH 20214 159 33 line line NN 20214 159 34 , , , 20214 159 35 and and CC 20214 159 36 then then RB 20214 159 37 move move VB 20214 159 38 the the DT 20214 159 39 indicator indicator NN 20214 159 40 to to IN 20214 159 41 2 2 CD 20214 159 42 on on IN 20214 159 43 the the DT 20214 159 44 C C NNP 20214 159 45 scale scale NN 20214 159 46 . . . 20214 160 1 Thus thus RB 20214 160 2 , , , 20214 160 3 successive successive JJ 20214 160 4 division division NN 20214 160 5 and and CC 20214 160 6 multiplication multiplication NN 20214 160 7 is be VBZ 20214 160 8 continued continue VBN 20214 160 9 until until IN 20214 160 10 all all PDT 20214 160 11 the the DT 20214 160 12 factors factor NNS 20214 160 13 have have VBP 20214 160 14 been be VBN 20214 160 15 used use VBN 20214 160 16 . . . 20214 161 1 The the DT 20214 161 2 order order NN 20214 161 3 in in IN 20214 161 4 which which WDT 20214 161 5 the the DT 20214 161 6 factors factor NNS 20214 161 7 are be VBP 20214 161 8 taken take VBN 20214 161 9 does do VBZ 20214 161 10 not not RB 20214 161 11 affect affect VB 20214 161 12 the the DT 20214 161 13 result result NN 20214 161 14 . . . 20214 162 1 With with IN 20214 162 2 a a DT 20214 162 3 little little JJ 20214 162 4 practice practice NN 20214 162 5 you -PRON- PRP 20214 162 6 will will MD 20214 162 7 learn learn VB 20214 162 8 to to TO 20214 162 9 take take VB 20214 162 10 them -PRON- PRP 20214 162 11 in in IN 20214 162 12 the the DT 20214 162 13 order order NN 20214 162 14 which which WDT 20214 162 15 will will MD 20214 162 16 require require VB 20214 162 17 the the DT 20214 162 18 fewest few JJS 20214 162 19 settings setting NNS 20214 162 20 . . . 20214 163 1 The the DT 20214 163 2 following follow VBG 20214 163 3 examples example NNS 20214 163 4 are be VBP 20214 163 5 for for IN 20214 163 6 practice practice NN 20214 163 7 : : : 20214 163 8 Example example NN 20214 163 9 56 56 CD 20214 163 10 : : : 20214 163 11 ( ( -LRB- 20214 163 12 6/3.5 6/3.5 LS 20214 163 13 ) ) -RRB- 20214 163 14 * * NFP 20214 163 15 ( ( -LRB- 20214 163 16 4/5 4/5 CD 20214 163 17 ) ) -RRB- 20214 163 18 * * NFP 20214 163 19 ( ( -LRB- 20214 163 20 3.5/2.4 3.5/2.4 CD 20214 163 21 ) ) -RRB- 20214 163 22 * * NFP 20214 163 23 ( ( -LRB- 20214 163 24 2.8/7 2.8/7 CD 20214 163 25 ) ) -RRB- 20214 163 26 = = NFP 20214 163 27 .8 .8 . 20214 163 28 Example example NN 20214 163 29 57 57 CD 20214 163 30 : : : 20214 163 31 352 352 CD 20214 163 32 * * NFP 20214 163 33 ( ( -LRB- 20214 163 34 273/254 273/254 NNP 20214 163 35 ) ) -RRB- 20214 163 36 * * NFP 20214 163 37 ( ( -LRB- 20214 163 38 760/768 760/768 NNP 20214 163 39 ) ) -RRB- 20214 163 40 = = NFP 20214 163 41 374 374 CD 20214 163 42 An an DT 20214 163 43 alternative alternative JJ 20214 163 44 method method NN 20214 163 45 of of IN 20214 163 46 doing do VBG 20214 163 47 these these DT 20214 163 48 examples example NNS 20214 163 49 is be VBZ 20214 163 50 to to TO 20214 163 51 proceed proceed VB 20214 163 52 exactly exactly RB 20214 163 53 as as IN 20214 163 54 though though IN 20214 163 55 you -PRON- PRP 20214 163 56 were be VBD 20214 163 57 multiplying multiply VBG 20214 163 58 all all PDT 20214 163 59 the the DT 20214 163 60 factors factor NNS 20214 163 61 together together RB 20214 163 62 , , , 20214 163 63 except except IN 20214 163 64 that that IN 20214 163 65 whenever whenever WRB 20214 163 66 you -PRON- PRP 20214 163 67 come come VBP 20214 163 68 to to IN 20214 163 69 a a DT 20214 163 70 number number NN 20214 163 71 in in IN 20214 163 72 the the DT 20214 163 73 denominator denominator NN 20214 163 74 you -PRON- PRP 20214 163 75 use use VBP 20214 163 76 the the DT 20214 163 77 CI CI NNP 20214 163 78 scale scale NN 20214 163 79 instead instead RB 20214 163 80 of of IN 20214 163 81 the the DT 20214 163 82 C C NNP 20214 163 83 scale scale NN 20214 163 84 . . . 20214 164 1 The the DT 20214 164 2 reader reader NN 20214 164 3 is be VBZ 20214 164 4 advised advise VBN 20214 164 5 to to TO 20214 164 6 practice practice VB 20214 164 7 both both DT 20214 164 8 methods method NNS 20214 164 9 and and CC 20214 164 10 use use VBP 20214 164 11 whichever whichever WDT 20214 164 12 one one NN 20214 164 13 he -PRON- PRP 20214 164 14 likes like VBZ 20214 164 15 best well RBS 20214 164 16 . . . 20214 165 1 3 3 LS 20214 165 2 . . . 20214 166 1 The the DT 20214 166 2 area area NN 20214 166 3 of of IN 20214 166 4 a a DT 20214 166 5 circle circle NN 20214 166 6 . . . 20214 167 1 The the DT 20214 167 2 area area NN 20214 167 3 of of IN 20214 167 4 a a DT 20214 167 5 circle circle NN 20214 167 6 is be VBZ 20214 167 7 found find VBN 20214 167 8 by by IN 20214 167 9 multiplying multiply VBG 20214 167 10 3.1416 3.1416 CD 20214 167 11 = = SYM 20214 167 12 PI pi NN 20214 167 13 by by IN 20214 167 14 the the DT 20214 167 15 square square NN 20214 167 16 of of IN 20214 167 17 the the DT 20214 167 18 radius radius NN 20214 167 19 or or CC 20214 167 20 by by IN 20214 167 21 one one CD 20214 167 22 - - HYPH 20214 167 23 quarter quarter NN 20214 167 24 the the DT 20214 167 25 square square NN 20214 167 26 of of IN 20214 167 27 the the DT 20214 167 28 diameter diameter NN 20214 167 29 Formula Formula NNP 20214 167 30 : : : 20214 167 31 A a NN 20214 167 32 = = SYM 20214 167 33 PI pi NN 20214 167 34 * * NFP 20214 167 35 square square NN 20214 167 36 ( ( -LRB- 20214 167 37 R r NN 20214 167 38 ) ) -RRB- 20214 167 39 A a NN 20214 167 40 = = SYM 20214 167 41 PI pi NN 20214 167 42 * * NFP 20214 167 43 ( ( -LRB- 20214 167 44 square square NN 20214 167 45 ( ( -LRB- 20214 167 46 D D NNP 20214 167 47 ) ) -RRB- 20214 167 48 / / SYM 20214 167 49 4 4 CD 20214 167 50 ) ) -RRB- 20214 167 51 Example example NN 20214 167 52 58 58 CD 20214 167 53 : : : 20214 167 54 The the DT 20214 167 55 radius radius NN 20214 167 56 of of IN 20214 167 57 a a DT 20214 167 58 circle circle NN 20214 167 59 is be VBZ 20214 167 60 0.25 0.25 CD 20214 167 61 inches inch NNS 20214 167 62 ; ; : 20214 167 63 find find VB 20214 167 64 its -PRON- PRP$ 20214 167 65 area area NN 20214 167 66 . . . 20214 168 1 Area area NN 20214 168 2 = = SYM 20214 168 3 PI pi NN 20214 168 4 * * NFP 20214 168 5 square(0.25 square(0.25 CD 20214 168 6 ) ) -RRB- 20214 168 7 = = NFP 20214 168 8 0.196 0.196 CD 20214 168 9 square square JJ 20214 168 10 inches inch NNS 20214 168 11 . . . 20214 169 1 Set Set VBN 20214 169 2 left left JJ 20214 169 3 - - HYPH 20214 169 4 hand hand NN 20214 169 5 index index NN 20214 169 6 of of IN 20214 169 7 C C NNP 20214 169 8 scale scale NN 20214 169 9 over over IN 20214 169 10 0.25 0.25 CD 20214 169 11 on on IN 20214 169 12 D d NN 20214 169 13 scale scale NN 20214 169 14 . . . 20214 170 1 square(0.25 square(0.25 LS 20214 170 2 ) ) -RRB- 20214 170 3 now now RB 20214 170 4 appears appear VBZ 20214 170 5 above above IN 20214 170 6 the the DT 20214 170 7 left left JJ 20214 170 8 - - HYPH 20214 170 9 hand hand NN 20214 170 10 index index NN 20214 170 11 of of IN 20214 170 12 the the DT 20214 170 13 B b NN 20214 170 14 scale scale NN 20214 170 15 . . . 20214 171 1 This this DT 20214 171 2 can can MD 20214 171 3 be be VB 20214 171 4 multiplied multiply VBN 20214 171 5 by by IN 20214 171 6 PI PI NNP 20214 171 7 by by IN 20214 171 8 moving move VBG 20214 171 9 the the DT 20214 171 10 indicator indicator NN 20214 171 11 to to IN 20214 171 12 PI PI NNP 20214 171 13 on on IN 20214 171 14 the the DT 20214 171 15 B b NN 20214 171 16 scale scale NN 20214 171 17 and and CC 20214 171 18 reading read VBG 20214 171 19 the the DT 20214 171 20 answer answer NN 20214 171 21 .196 .196 CD 20214 171 22 on on IN 20214 171 23 the the DT 20214 171 24 A a DT 20214 171 25 scale scale NN 20214 171 26 . . . 20214 172 1 This this DT 20214 172 2 is be VBZ 20214 172 3 an an DT 20214 172 4 example example NN 20214 172 5 where where WRB 20214 172 6 it -PRON- PRP 20214 172 7 is be VBZ 20214 172 8 convenient convenient JJ 20214 172 9 to to TO 20214 172 10 multiply multiply VB 20214 172 11 with with IN 20214 172 12 the the DT 20214 172 13 A a NN 20214 172 14 and and CC 20214 172 15 B b NN 20214 172 16 scales scale NNS 20214 172 17 . . . 20214 173 1 Example example NN 20214 173 2 59 59 CD 20214 173 3 : : : 20214 173 4 The the DT 20214 173 5 diameter diameter NN 20214 173 6 of of IN 20214 173 7 a a DT 20214 173 8 circle circle NN 20214 173 9 is be VBZ 20214 173 10 8.1 8.1 CD 20214 173 11 feet foot NNS 20214 173 12 . . . 20214 174 1 What what WP 20214 174 2 is be VBZ 20214 174 3 its -PRON- PRP$ 20214 174 4 area area NN 20214 174 5 ? ? . 20214 175 1 Area area NN 20214 175 2 = = NFP 20214 175 3 ( ( -LRB- 20214 175 4 PI pi NN 20214 175 5 / / SYM 20214 175 6 4 4 CD 20214 175 7 ) ) -RRB- 20214 175 8 * * NFP 20214 175 9 square(8.1 square(8.1 CD 20214 175 10 ) ) -RRB- 20214 175 11 = = NFP 20214 175 12 .7854 .7854 NFP 20214 175 13 * * NFP 20214 175 14 square(8.1 square(8.1 CD 20214 175 15 ) ) -RRB- 20214 175 16 = = NFP 20214 175 17 51.7 51.7 CD 20214 175 18 sq sq NN 20214 175 19 . . . 20214 176 1 inches inch NNS 20214 176 2 . . . 20214 177 1 Set Set VBN 20214 177 2 right right JJ 20214 177 3 - - HYPH 20214 177 4 hand hand NN 20214 177 5 index index NN 20214 177 6 of of IN 20214 177 7 the the DT 20214 177 8 C C NNP 20214 177 9 scale scale NN 20214 177 10 over over IN 20214 177 11 8.1 8.1 CD 20214 177 12 on on IN 20214 177 13 the the DT 20214 177 14 D d JJ 20214 177 15 scale scale NN 20214 177 16 . . . 20214 178 1 Move move VB 20214 178 2 the the DT 20214 178 3 indicator indicator NN 20214 178 4 till till IN 20214 178 5 hair hair NN 20214 178 6 - - HYPH 20214 178 7 line line NN 20214 178 8 is be VBZ 20214 178 9 over over RB 20214 178 10 .7854 .7854 . 20214 178 11 ( ( -LRB- 20214 178 12 the the DT 20214 178 13 special special JJ 20214 178 14 long long JJ 20214 178 15 mark mark NN 20214 178 16 near near IN 20214 178 17 8) 8) CD 20214 178 18 at at IN 20214 178 19 the the DT 20214 178 20 right right JJ 20214 178 21 hand hand NN 20214 178 22 of of IN 20214 178 23 the the DT 20214 178 24 B b NN 20214 178 25 scale scale NN 20214 178 26 . . . 20214 179 1 Read read VB 20214 179 2 the the DT 20214 179 3 answer answer NN 20214 179 4 under under IN 20214 179 5 the the DT 20214 179 6 hair hair NN 20214 179 7 - - HYPH 20214 179 8 line line NN 20214 179 9 on on IN 20214 179 10 the the DT 20214 179 11 A a DT 20214 179 12 scale scale NN 20214 179 13 . . . 20214 180 1 Another another DT 20214 180 2 way way NN 20214 180 3 of of IN 20214 180 4 finding find VBG 20214 180 5 the the DT 20214 180 6 area area NN 20214 180 7 of of IN 20214 180 8 a a DT 20214 180 9 circle circle NN 20214 180 10 is be VBZ 20214 180 11 to to TO 20214 180 12 set set VB 20214 180 13 7854 7854 CD 20214 180 14 on on IN 20214 180 15 the the DT 20214 180 16 B b NN 20214 180 17 scale scale NN 20214 180 18 to to IN 20214 180 19 one one CD 20214 180 20 of of IN 20214 180 21 the the DT 20214 180 22 indices index NNS 20214 180 23 of of IN 20214 180 24 the the DT 20214 180 25 A a DT 20214 180 26 scale scale NN 20214 180 27 , , , 20214 180 28 and and CC 20214 180 29 read read VBD 20214 180 30 the the DT 20214 180 31 area area NN 20214 180 32 from from IN 20214 180 33 the the DT 20214 180 34 B b NN 20214 180 35 scale scale NN 20214 180 36 directly directly RB 20214 180 37 above above IN 20214 180 38 the the DT 20214 180 39 given give VBN 20214 180 40 diameter diameter NN 20214 180 41 on on IN 20214 180 42 the the DT 20214 180 43 D d JJ 20214 180 44 scale scale NN 20214 180 45 . . . 20214 181 1 4 4 LS 20214 181 2 . . . 20214 182 1 The the DT 20214 182 2 circumference circumference NN 20214 182 3 of of IN 20214 182 4 a a DT 20214 182 5 circle circle NN 20214 182 6 . . . 20214 183 1 Set Set VBN 20214 183 2 the the DT 20214 183 3 index index NN 20214 183 4 of of IN 20214 183 5 the the DT 20214 183 6 B B NNP 20214 183 7 scale scale NN 20214 183 8 to to IN 20214 183 9 the the DT 20214 183 10 diameter diameter NN 20214 183 11 and and CC 20214 183 12 read read VB 20214 183 13 the the DT 20214 183 14 answer answer NN 20214 183 15 on on IN 20214 183 16 the the DT 20214 183 17 A a DT 20214 183 18 scale scale NN 20214 183 19 opposite opposite JJ 20214 183 20 PI pi NN 20214 183 21 on on IN 20214 183 22 the the DT 20214 183 23 B b NN 20214 183 24 scale scale NN 20214 183 25 Formula formula NN 20214 183 26 : : : 20214 183 27 C C NNP 20214 183 28 = = SYM 20214 183 29 PI pi NN 20214 183 30 * * NFP 20214 183 31 D d NN 20214 183 32 C c NN 20214 183 33 = = SYM 20214 183 34 2 2 CD 20214 183 35 * * NFP 20214 183 36 PI pi NN 20214 183 37 * * NFP 20214 183 38 R r NN 20214 183 39 Example example NN 20214 183 40 60 60 CD 20214 183 41 : : : 20214 183 42 The the DT 20214 183 43 diameter diameter NN 20214 183 44 of of IN 20214 183 45 a a DT 20214 183 46 circle circle NN 20214 183 47 is be VBZ 20214 183 48 1.54 1.54 CD 20214 183 49 inches inch NNS 20214 183 50 , , , 20214 183 51 what what WP 20214 183 52 is be VBZ 20214 183 53 its -PRON- PRP$ 20214 183 54 circumference circumference NN 20214 183 55 ? ? . 20214 184 1 Set set VB 20214 184 2 the the DT 20214 184 3 left left JJ 20214 184 4 - - HYPH 20214 184 5 hand hand NN 20214 184 6 index index NN 20214 184 7 of of IN 20214 184 8 the the DT 20214 184 9 B B NNP 20214 184 10 scale scale NN 20214 184 11 to to IN 20214 184 12 1.54 1.54 CD 20214 184 13 on on IN 20214 184 14 the the DT 20214 184 15 A a DT 20214 184 16 scale scale NN 20214 184 17 . . . 20214 185 1 Read read VB 20214 185 2 the the DT 20214 185 3 circumference circumference NN 20214 185 4 4.85 4.85 CD 20214 185 5 inches inch NNS 20214 185 6 above above IN 20214 185 7 PI pi NN 20214 185 8 on on IN 20214 185 9 the the DT 20214 185 10 B b NN 20214 185 11 scale scale NN 20214 185 12 . . . 20214 186 1 EXAMPLES examples VB 20214 186 2 FOR for IN 20214 186 3 PRACTICE practice NN 20214 186 4 61 61 CD 20214 186 5 : : : 20214 186 6 What what WP 20214 186 7 is be VBZ 20214 186 8 the the DT 20214 186 9 area area NN 20214 186 10 of of IN 20214 186 11 a a DT 20214 186 12 circle circle NN 20214 186 13 32 32 CD 20214 186 14 - - HYPH 20214 186 15 1/2 1/2 CD 20214 186 16 inches inch NNS 20214 186 17 in in IN 20214 186 18 diameter diameter NN 20214 186 19 ? ? . 20214 187 1 Answer Answer NNP 20214 187 2 830 830 CD 20214 187 3 sq sq NN 20214 187 4 . . . 20214 188 1 inches inch NNS 20214 188 2 62 62 CD 20214 188 3 : : : 20214 188 4 What what WP 20214 188 5 is be VBZ 20214 188 6 the the DT 20214 188 7 area area NN 20214 188 8 of of IN 20214 188 9 a a DT 20214 188 10 circle circle NN 20214 188 11 24 24 CD 20214 188 12 inches inch NNS 20214 188 13 in in IN 20214 188 14 diameter diameter NN 20214 188 15 ? ? . 20214 189 1 Answer Answer NNP 20214 189 2 452 452 CD 20214 189 3 sq sq NN 20214 189 4 . . . 20214 190 1 inches inch NNS 20214 190 2 63 63 CD 20214 190 3 : : : 20214 190 4 What what WP 20214 190 5 is be VBZ 20214 190 6 the the DT 20214 190 7 circumference circumference NN 20214 190 8 of of IN 20214 190 9 a a DT 20214 190 10 circle circle NN 20214 190 11 whose whose WP$ 20214 190 12 diameter diameter NN 20214 190 13 is be VBZ 20214 190 14 95 95 CD 20214 190 15 feet foot NNS 20214 190 16 ? ? . 20214 191 1 Answer Answer NNP 20214 191 2 298 298 CD 20214 191 3 ft ft NN 20214 191 4 . . NNP 20214 191 5 64 64 CD 20214 191 6 : : : 20214 191 7 What what WP 20214 191 8 is be VBZ 20214 191 9 the the DT 20214 191 10 circumference circumference NN 20214 191 11 of of IN 20214 191 12 a a DT 20214 191 13 circle circle NN 20214 191 14 whose whose WP$ 20214 191 15 diameter diameter NN 20214 191 16 is be VBZ 20214 191 17 3.65 3.65 CD 20214 191 18 inches inch NNS 20214 191 19 ? ? . 20214 192 1 Answer answer NN 20214 192 2 11.5 11.5 CD 20214 192 3 inches inch NNS 20214 192 4 5 5 CD 20214 192 5 . . . 20214 193 1 Ratio ratio NN 20214 193 2 and and CC 20214 193 3 Proportion proportion NN 20214 193 4 . . . 20214 194 1 Example example NN 20214 194 2 65 65 CD 20214 194 3 : : SYM 20214 194 4 3 3 CD 20214 194 5 : : SYM 20214 194 6 7 7 CD 20214 194 7 : : : 20214 194 8 : : : 20214 194 9 4 4 LS 20214 194 10 : : : 20214 194 11 X x NN 20214 194 12 or or CC 20214 194 13 ( ( -LRB- 20214 194 14 3/7 3/7 CD 20214 194 15 ) ) -RRB- 20214 194 16 = = NFP 20214 194 17 ( ( -LRB- 20214 194 18 4 4 CD 20214 194 19 / / SYM 20214 194 20 x x LS 20214 194 21 ) ) -RRB- 20214 194 22 Find Find NNP 20214 194 23 X x NN 20214 194 24 Set set NN 20214 194 25 3 3 CD 20214 194 26 on on IN 20214 194 27 C c NN 20214 194 28 scale scale NN 20214 194 29 over over IN 20214 194 30 7 7 CD 20214 194 31 on on IN 20214 194 32 D d NN 20214 194 33 scale scale NN 20214 194 34 . . . 20214 195 1 Read read VB 20214 195 2 X x NN 20214 195 3 on on IN 20214 195 4 D d JJ 20214 195 5 scale scale NN 20214 195 6 under under IN 20214 195 7 4 4 CD 20214 195 8 on on IN 20214 195 9 C c NN 20214 195 10 scale scale NN 20214 195 11 . . . 20214 196 1 In in IN 20214 196 2 fact fact NN 20214 196 3 , , , 20214 196 4 any any DT 20214 196 5 number number NN 20214 196 6 on on IN 20214 196 7 the the DT 20214 196 8 C C NNP 20214 196 9 scale scale NN 20214 196 10 is be VBZ 20214 196 11 to to IN 20214 196 12 the the DT 20214 196 13 number number NN 20214 196 14 directly directly RB 20214 196 15 under under IN 20214 196 16 it -PRON- PRP 20214 196 17 on on IN 20214 196 18 the the DT 20214 196 19 D d JJ 20214 196 20 scale scale NN 20214 196 21 as as IN 20214 196 22 3 3 CD 20214 196 23 is be VBZ 20214 196 24 to to IN 20214 196 25 7 7 CD 20214 196 26 . . . 20214 197 1 PRACTICAL practical NN 20214 197 2 PROBLEMS problem NNS 20214 197 3 SOLVED solve VBN 20214 197 4 BY by IN 20214 197 5 SLIDE SLIDE NNP 20214 197 6 RULE RULE NNP 20214 197 7 1 1 CD 20214 197 8 . . . 20214 198 1 Discount discount NN 20214 198 2 . . . 20214 199 1 A a DT 20214 199 2 firm firm NN 20214 199 3 buys buy VBZ 20214 199 4 a a DT 20214 199 5 typewriter typewriter NN 20214 199 6 with with IN 20214 199 7 a a DT 20214 199 8 list list NN 20214 199 9 price price NN 20214 199 10 of of IN 20214 199 11 $ $ $ 20214 199 12 150 150 CD 20214 199 13 , , , 20214 199 14 subject subject JJ 20214 199 15 to to IN 20214 199 16 a a DT 20214 199 17 discount discount NN 20214 199 18 of of IN 20214 199 19 20 20 CD 20214 199 20 % % NN 20214 199 21 and and CC 20214 199 22 10 10 CD 20214 199 23 % % NN 20214 199 24 . . . 20214 200 1 How how WRB 20214 200 2 much much JJ 20214 200 3 does do VBZ 20214 200 4 it -PRON- PRP 20214 200 5 pay pay VB 20214 200 6 ? ? . 20214 201 1 A a DT 20214 201 2 discount discount NN 20214 201 3 of of IN 20214 201 4 20 20 CD 20214 201 5 % % NN 20214 201 6 means mean VBZ 20214 201 7 0.8 0.8 CD 20214 201 8 of of IN 20214 201 9 the the DT 20214 201 10 list list NN 20214 201 11 price price NN 20214 201 12 , , , 20214 201 13 and and CC 20214 201 14 10 10 CD 20214 201 15 % % NN 20214 201 16 more more JJR 20214 201 17 means mean NNS 20214 201 18 0.8 0.8 CD 20214 201 19 X x NN 20214 201 20 0.9 0.9 CD 20214 201 21 X x NN 20214 201 22 150 150 CD 20214 201 23 = = SYM 20214 201 24 108 108 CD 20214 201 25 . . . 20214 202 1 To to TO 20214 202 2 do do VB 20214 202 3 this this DT 20214 202 4 on on IN 20214 202 5 the the DT 20214 202 6 slide slide NN 20214 202 7 rule rule NN 20214 202 8 , , , 20214 202 9 put put VBD 20214 202 10 the the DT 20214 202 11 index index NN 20214 202 12 of of IN 20214 202 13 the the DT 20214 202 14 C C NNP 20214 202 15 scale scale NN 20214 202 16 opposite opposite JJ 20214 202 17 8 8 CD 20214 202 18 on on IN 20214 202 19 the the DT 20214 202 20 D d JJ 20214 202 21 scale scale NN 20214 202 22 and and CC 20214 202 23 move move VB 20214 202 24 the the DT 20214 202 25 indicator indicator NN 20214 202 26 to to IN 20214 202 27 9 9 CD 20214 202 28 on on IN 20214 202 29 the the DT 20214 202 30 C C NNP 20214 202 31 scale scale NN 20214 202 32 . . . 20214 203 1 Then then RB 20214 203 2 move move VB 20214 203 3 the the DT 20214 203 4 slider slider NN 20214 203 5 till till IN 20214 203 6 the the DT 20214 203 7 right right JJ 20214 203 8 - - HYPH 20214 203 9 hand hand NN 20214 203 10 index index NN 20214 203 11 of of IN 20214 203 12 the the DT 20214 203 13 C C NNP 20214 203 14 scale scale NN 20214 203 15 is be VBZ 20214 203 16 under under IN 20214 203 17 the the DT 20214 203 18 hairline hairline NN 20214 203 19 . . . 20214 204 1 Now now RB 20214 204 2 , , , 20214 204 3 move move VB 20214 204 4 the the DT 20214 204 5 indicator indicator NN 20214 204 6 to to IN 20214 204 7 150 150 CD 20214 204 8 on on IN 20214 204 9 the the DT 20214 204 10 C C NNP 20214 204 11 scale scale NN 20214 204 12 and and CC 20214 204 13 read read VB 20214 204 14 the the DT 20214 204 15 answer answer NN 20214 204 16 $ $ $ 20214 204 17 108 108 CD 20214 204 18 on on IN 20214 204 19 the the DT 20214 204 20 D d JJ 20214 204 21 scale scale NN 20214 204 22 . . . 20214 205 1 Notice notice VB 20214 205 2 that that IN 20214 205 3 in in IN 20214 205 4 this this DT 20214 205 5 , , , 20214 205 6 as as IN 20214 205 7 in in IN 20214 205 8 many many JJ 20214 205 9 practical practical JJ 20214 205 10 problems problem NNS 20214 205 11 , , , 20214 205 12 there there EX 20214 205 13 is be VBZ 20214 205 14 no no DT 20214 205 15 question question NN 20214 205 16 about about IN 20214 205 17 where where WRB 20214 205 18 the the DT 20214 205 19 decimal decimal JJ 20214 205 20 point point NN 20214 205 21 should should MD 20214 205 22 go go VB 20214 205 23 . . . 20214 206 1 2 2 LS 20214 206 2 . . . 20214 207 1 Sales sale NNS 20214 207 2 Tax Tax NNP 20214 207 3 . . . 20214 208 1 A a DT 20214 208 2 man man NN 20214 208 3 buys buy VBZ 20214 208 4 an an DT 20214 208 5 article article NN 20214 208 6 worth worth JJ 20214 208 7 $ $ $ 20214 208 8 12 12 CD 20214 208 9 and and CC 20214 208 10 he -PRON- PRP 20214 208 11 must must MD 20214 208 12 pay pay VB 20214 208 13 a a DT 20214 208 14 sales sale NNS 20214 208 15 tax tax NN 20214 208 16 of of IN 20214 208 17 1.5 1.5 CD 20214 208 18 % % NN 20214 208 19 . . . 20214 209 1 How how WRB 20214 209 2 much much JJ 20214 209 3 does do VBZ 20214 209 4 he -PRON- PRP 20214 209 5 pay pay VB 20214 209 6 ? ? . 20214 210 1 A a DT 20214 210 2 tax tax NN 20214 210 3 of of IN 20214 210 4 1.5 1.5 CD 20214 210 5 % % NN 20214 210 6 means mean VBZ 20214 210 7 he -PRON- PRP 20214 210 8 must must MD 20214 210 9 pay pay VB 20214 210 10 1.015 1.015 CD 20214 210 11 * * NFP 20214 210 12 12.00 12.00 CD 20214 210 13 . . . 20214 211 1 Set Set VBN 20214 211 2 index index NN 20214 211 3 of of IN 20214 211 4 C C NNP 20214 211 5 scale scale NN 20214 211 6 at at IN 20214 211 7 1.015 1.015 CD 20214 211 8 on on IN 20214 211 9 D d JJ 20214 211 10 scale scale NN 20214 211 11 . . . 20214 212 1 Move move NN 20214 212 2 indicator indicator NN 20214 212 3 to to IN 20214 212 4 12 12 CD 20214 212 5 on on IN 20214 212 6 C c NN 20214 212 7 scale scale NN 20214 212 8 and and CC 20214 212 9 read read VB 20214 212 10 the the DT 20214 212 11 answer answer NN 20214 212 12 $ $ $ 20214 212 13 12.18 12.18 CD 20214 212 14 on on IN 20214 212 15 the the DT 20214 212 16 D d JJ 20214 212 17 scale scale NN 20214 212 18 . . . 20214 213 1 A a DT 20214 213 2 longer long JJR 20214 213 3 but but CC 20214 213 4 more more RBR 20214 213 5 accurate accurate JJ 20214 213 6 way way NN 20214 213 7 is be VBZ 20214 213 8 to to TO 20214 213 9 multiply multiply VB 20214 213 10 12 12 CD 20214 213 11 * * NFP 20214 213 12 .015 .015 CD 20214 213 13 and and CC 20214 213 14 add add VB 20214 213 15 the the DT 20214 213 16 result result NN 20214 213 17 to to IN 20214 213 18 $ $ $ 20214 213 19 12 12 CD 20214 213 20 . . . 20214 214 1 3 3 LS 20214 214 2 . . . 20214 215 1 Unit Unit NNP 20214 215 2 Price Price NNP 20214 215 3 . . . 20214 216 1 A a DT 20214 216 2 motorist motorist NN 20214 216 3 buys buy VBZ 20214 216 4 17 17 CD 20214 216 5 gallons gallon NNS 20214 216 6 of of IN 20214 216 7 gas gas NN 20214 216 8 at at IN 20214 216 9 19.5 19.5 CD 20214 216 10 cents cent NNS 20214 216 11 per per IN 20214 216 12 gallon gallon NN 20214 216 13 . . . 20214 217 1 How how WRB 20214 217 2 much much JJ 20214 217 3 does do VBZ 20214 217 4 he -PRON- PRP 20214 217 5 pay pay VB 20214 217 6 ? ? . 20214 218 1 Set Set VBN 20214 218 2 index index NN 20214 218 3 of of IN 20214 218 4 C C NNP 20214 218 5 scale scale NN 20214 218 6 at at IN 20214 218 7 17 17 CD 20214 218 8 on on IN 20214 218 9 D d NN 20214 218 10 scale scale NN 20214 218 11 and and CC 20214 218 12 move move NN 20214 218 13 indicator indicator NN 20214 218 14 to to IN 20214 218 15 19.5 19.5 CD 20214 218 16 on on IN 20214 218 17 C c NN 20214 218 18 scale scale NN 20214 218 19 and and CC 20214 218 20 read read VB 20214 218 21 the the DT 20214 218 22 answer answer NN 20214 218 23 $ $ $ 20214 218 24 3.32 3.32 CD 20214 218 25 on on IN 20214 218 26 the the DT 20214 218 27 D d JJ 20214 218 28 scale scale NN 20214 218 29 . . . 20214 219 1 4 4 LS 20214 219 2 . . . 20214 220 1 Gasoline Gasoline NNP 20214 220 2 Mileage Mileage NNP 20214 220 3 . . . 20214 221 1 An an DT 20214 221 2 automobile automobile NN 20214 221 3 goes go VBZ 20214 221 4 175 175 CD 20214 221 5 miles mile NNS 20214 221 6 on on IN 20214 221 7 12 12 CD 20214 221 8 gallons gallon NNS 20214 221 9 of of IN 20214 221 10 gas gas NN 20214 221 11 . . . 20214 222 1 What what WP 20214 222 2 is be VBZ 20214 222 3 the the DT 20214 222 4 average average JJ 20214 222 5 gasoline gasoline NN 20214 222 6 consumption consumption NN 20214 222 7 ? ? . 20214 223 1 Set Set VBN 20214 223 2 indicator indicator NN 20214 223 3 over over IN 20214 223 4 175 175 CD 20214 223 5 on on IN 20214 223 6 D d NN 20214 223 7 scale scale NN 20214 223 8 and and CC 20214 223 9 move move NN 20214 223 10 slider slider NN 20214 223 11 till till IN 20214 223 12 12 12 CD 20214 223 13 is be VBZ 20214 223 14 under under IN 20214 223 15 hair hair NN 20214 223 16 - - HYPH 20214 223 17 line line NN 20214 223 18 . . . 20214 224 1 Read read VB 20214 224 2 the the DT 20214 224 3 answer answer NN 20214 224 4 14.6 14.6 CD 20214 224 5 miles mile NNS 20214 224 6 per per IN 20214 224 7 gallon gallon NN 20214 224 8 on on IN 20214 224 9 the the DT 20214 224 10 D d JJ 20214 224 11 scale scale NN 20214 224 12 under under IN 20214 224 13 the the DT 20214 224 14 left left JJ 20214 224 15 - - HYPH 20214 224 16 hand hand NN 20214 224 17 index index NN 20214 224 18 of of IN 20214 224 19 the the DT 20214 224 20 C C NNP 20214 224 21 scale scale NN 20214 224 22 . . . 20214 225 1 5 5 CD 20214 225 2 . . . 20214 226 1 Average average JJ 20214 226 2 Speed speed NN 20214 226 3 . . . 20214 227 1 A a DT 20214 227 2 motorist motorist NN 20214 227 3 makes make VBZ 20214 227 4 a a DT 20214 227 5 trip trip NN 20214 227 6 of of IN 20214 227 7 256 256 CD 20214 227 8 miles mile NNS 20214 227 9 in in IN 20214 227 10 7.5 7.5 CD 20214 227 11 hours hour NNS 20214 227 12 . . . 20214 228 1 What what WP 20214 228 2 is be VBZ 20214 228 3 his -PRON- PRP$ 20214 228 4 average average JJ 20214 228 5 speed speed NN 20214 228 6 ? ? . 20214 229 1 Set Set VBN 20214 229 2 indicator indicator NN 20214 229 3 over over IN 20214 229 4 256 256 CD 20214 229 5 on on IN 20214 229 6 D d JJ 20214 229 7 scale scale NN 20214 229 8 . . . 20214 230 1 Move move VB 20214 230 2 slider slider NN 20214 230 3 till till IN 20214 230 4 7.5 7.5 CD 20214 230 5 on on IN 20214 230 6 the the DT 20214 230 7 C C NNP 20214 230 8 scale scale NN 20214 230 9 is be VBZ 20214 230 10 under under IN 20214 230 11 the the DT 20214 230 12 hair hair NN 20214 230 13 - - HYPH 20214 230 14 line line NN 20214 230 15 . . . 20214 231 1 Read read VB 20214 231 2 the the DT 20214 231 3 answer answer NN 20214 231 4 34.2 34.2 CD 20214 231 5 miles mile NNS 20214 231 6 per per IN 20214 231 7 hour hour NN 20214 231 8 under under IN 20214 231 9 the the DT 20214 231 10 right right JJ 20214 231 11 - - HYPH 20214 231 12 hand hand NN 20214 231 13 index index NN 20214 231 14 of of IN 20214 231 15 the the DT 20214 231 16 C C NNP 20214 231 17 scale scale NN 20214 231 18 . . . 20214 232 1 6 6 CD 20214 232 2 . . . 20214 233 1 Decimal Decimal NNP 20214 233 2 Parts Parts NNPS 20214 233 3 of of IN 20214 233 4 an an DT 20214 233 5 Inch Inch NNP 20214 233 6 . . . 20214 234 1 What what WP 20214 234 2 is be VBZ 20214 234 3 5/16 5/16 CD 20214 234 4 of of IN 20214 234 5 an an DT 20214 234 6 inch inch NN 20214 234 7 expressed express VBN 20214 234 8 as as IN 20214 234 9 decimal decimal JJ 20214 234 10 fraction fraction NN 20214 234 11 ? ? . 20214 235 1 Set Set VBN 20214 235 2 16 16 CD 20214 235 3 on on IN 20214 235 4 C c NN 20214 235 5 scale scale NN 20214 235 6 over over IN 20214 235 7 5 5 CD 20214 235 8 on on IN 20214 235 9 D d JJ 20214 235 10 scale scale NN 20214 235 11 and and CC 20214 235 12 read read VB 20214 235 13 the the DT 20214 235 14 result result NN 20214 235 15 .3125 .3125 . 20214 235 16 inches inch NNS 20214 235 17 on on IN 20214 235 18 the the DT 20214 235 19 D d JJ 20214 235 20 scale scale NN 20214 235 21 under under IN 20214 235 22 the the DT 20214 235 23 left left JJ 20214 235 24 - - HYPH 20214 235 25 hand hand NN 20214 235 26 index index NN 20214 235 27 of of IN 20214 235 28 the the DT 20214 235 29 C C NNP 20214 235 30 scale scale NN 20214 235 31 . . . 20214 236 1 7 7 LS 20214 236 2 . . . 20214 237 1 Physics physics NN 20214 237 2 . . . 20214 238 1 A a DT 20214 238 2 certain certain JJ 20214 238 3 quantity quantity NN 20214 238 4 of of IN 20214 238 5 gas gas NN 20214 238 6 occupies occupie NNS 20214 238 7 1200 1200 CD 20214 238 8 cubic cubic JJ 20214 238 9 centimeters centimeter NNS 20214 238 10 at at IN 20214 238 11 a a DT 20214 238 12 temperature temperature NN 20214 238 13 of of IN 20214 238 14 15 15 CD 20214 238 15 degrees degree NNS 20214 238 16 C c NN 20214 238 17 and and CC 20214 238 18 740 740 CD 20214 238 19 millimeters millimeter NNS 20214 238 20 pressure pressure NN 20214 238 21 . . . 20214 239 1 What what WDT 20214 239 2 volume volume NN 20214 239 3 does do VBZ 20214 239 4 it -PRON- PRP 20214 239 5 occupy occupy VB 20214 239 6 at at IN 20214 239 7 0 0 CD 20214 239 8 degrees degree NNS 20214 239 9 C c NN 20214 239 10 and and CC 20214 239 11 760 760 CD 20214 239 12 millimeters millimeter NNS 20214 239 13 pressure pressure NN 20214 239 14 ? ? . 20214 240 1 Volume volume NN 20214 240 2 = = SYM 20214 240 3 1200 1200 CD 20214 240 4 X x NN 20214 240 5 ( ( -LRB- 20214 240 6 740/760 740/760 NN 20214 240 7 ) ) -RRB- 20214 240 8 * * NFP 20214 240 9 ( ( -LRB- 20214 240 10 273/288 273/288 NN 20214 240 11 ) ) -RRB- 20214 240 12 = = NFP 20214 240 13 1100 1100 CD 20214 240 14 cubic cubic JJ 20214 240 15 cm cm NNS 20214 240 16 . . . 20214 241 1 Set Set NNP 20214 241 2 760 760 CD 20214 241 3 on on IN 20214 241 4 C c NN 20214 241 5 scale scale NN 20214 241 6 over over IN 20214 241 7 12 12 CD 20214 241 8 on on IN 20214 241 9 D d JJ 20214 241 10 scale scale NN 20214 241 11 . . . 20214 242 1 Move move NN 20214 242 2 indicator indicator NN 20214 242 3 to to IN 20214 242 4 740 740 CD 20214 242 5 on on IN 20214 242 6 C c NN 20214 242 7 scale scale NN 20214 242 8 . . . 20214 243 1 Move move VB 20214 243 2 slider slider NN 20214 243 3 till till IN 20214 243 4 288 288 CD 20214 243 5 on on IN 20214 243 6 C c NN 20214 243 7 scale scale NN 20214 243 8 is be VBZ 20214 243 9 under under IN 20214 243 10 hair hair NN 20214 243 11 - - HYPH 20214 243 12 line line NN 20214 243 13 . . . 20214 244 1 Move move NN 20214 244 2 indicator indicator NN 20214 244 3 to to IN 20214 244 4 273 273 CD 20214 244 5 on on IN 20214 244 6 C c NN 20214 244 7 scale scale NN 20214 244 8 . . . 20214 245 1 Read read VB 20214 245 2 answer answer NN 20214 245 3 , , , 20214 245 4 1110 1110 CD 20214 245 5 , , , 20214 245 6 under under IN 20214 245 7 hair hair NN 20214 245 8 - - HYPH 20214 245 9 line line NN 20214 245 10 on on IN 20214 245 11 D d JJ 20214 245 12 scale scale NN 20214 245 13 . . . 20214 246 1 8 8 LS 20214 246 2 . . . 20214 247 1 Chemistry chemistry NN 20214 247 2 . . . 20214 248 1 How how WRB 20214 248 2 many many JJ 20214 248 3 grams gram NNS 20214 248 4 of of IN 20214 248 5 hydrogen hydrogen NN 20214 248 6 are be VBP 20214 248 7 formed form VBN 20214 248 8 when when WRB 20214 248 9 80 80 CD 20214 248 10 grams gram NNS 20214 248 11 of of IN 20214 248 12 zinc zinc NN 20214 248 13 react react VBP 20214 248 14 with with IN 20214 248 15 sufficient sufficient JJ 20214 248 16 hydrochloric hydrochloric JJ 20214 248 17 acid acid NN 20214 248 18 to to TO 20214 248 19 dissolve dissolve VB 20214 248 20 the the DT 20214 248 21 metal metal NN 20214 248 22 ? ? . 20214 249 1 ( ( -LRB- 20214 249 2 80 80 CD 20214 249 3 / / SYM 20214 249 4 X x NN 20214 249 5 ) ) -RRB- 20214 249 6 = = NFP 20214 249 7 ( ( -LRB- 20214 249 8 65.4 65.4 CD 20214 249 9 / / SYM 20214 249 10 2.01 2.01 CD 20214 249 11 ) ) -RRB- 20214 249 12 Set Set VBN 20214 249 13 65.4 65.4 CD 20214 249 14 on on IN 20214 249 15 C C NNP 20214 249 16 scale scale NN 20214 249 17 over over IN 20214 249 18 2.01 2.01 CD 20214 249 19 on on IN 20214 249 20 D d JJ 20214 249 21 scale scale NN 20214 249 22 . . . 20214 250 1 Read read VB 20214 250 2 X X NNP 20214 250 3 = = SYM 20214 250 4 2.46 2.46 CD 20214 250 5 grams gram NNS 20214 250 6 under under IN 20214 250 7 80 80 CD 20214 250 8 on on IN 20214 250 9 C c NN 20214 250 10 scale scale NN 20214 250 11 . . . 20214 251 1 In in IN 20214 251 2 conclusion conclusion NN 20214 251 3 , , , 20214 251 4 we -PRON- PRP 20214 251 5 want want VBP 20214 251 6 to to TO 20214 251 7 impress impress VB 20214 251 8 upon upon IN 20214 251 9 those those DT 20214 251 10 to to TO 20214 251 11 whom whom WP 20214 251 12 the the DT 20214 251 13 slide slide NN 20214 251 14 rule rule NN 20214 251 15 is be VBZ 20214 251 16 a a DT 20214 251 17 new new JJ 20214 251 18 method method NN 20214 251 19 of of IN 20214 251 20 doing do VBG 20214 251 21 their -PRON- PRP$ 20214 251 22 mathematical mathematical JJ 20214 251 23 calculations calculation NNS 20214 251 24 , , , 20214 251 25 and and CC 20214 251 26 also also RB 20214 251 27 the the DT 20214 251 28 experienced experienced JJ 20214 251 29 operator operator NN 20214 251 30 of of IN 20214 251 31 a a DT 20214 251 32 slide slide NN 20214 251 33 rule rule NN 20214 251 34 , , , 20214 251 35 that that IN 20214 251 36 if if IN 20214 251 37 they -PRON- PRP 20214 251 38 will will MD 20214 251 39 form form VB 20214 251 40 a a DT 20214 251 41 habit habit NN 20214 251 42 of of IN 20214 251 43 , , , 20214 251 44 and and CC 20214 251 45 apply apply VB 20214 251 46 themselves -PRON- PRP 20214 251 47 to to IN 20214 251 48 , , , 20214 251 49 using use VBG 20214 251 50 a a DT 20214 251 51 slide slide NN 20214 251 52 rule rule NN 20214 251 53 at at IN 20214 251 54 work work NN 20214 251 55 , , , 20214 251 56 study study NN 20214 251 57 , , , 20214 251 58 or or CC 20214 251 59 during during IN 20214 251 60 recreations recreation NNS 20214 251 61 , , , 20214 251 62 they -PRON- PRP 20214 251 63 will will MD 20214 251 64 be be VB 20214 251 65 well well RB 20214 251 66 rewarded reward VBN 20214 251 67 in in IN 20214 251 68 the the DT 20214 251 69 saving saving NN 20214 251 70 of of IN 20214 251 71 time time NN 20214 251 72 and and CC 20214 251 73 energy energy NN 20214 251 74 . . . 20214 252 1 ALWAYS alway NNS 20214 252 2 HAVE have VBP 20214 252 3 YOUR your PRP$ 20214 252 4 SLIDE slide NN 20214 252 5 RULE rule NN 20214 252 6 AND and CC 20214 252 7 INSTRUCTION instruction NN 20214 252 8 BOOK BOOK NNP 20214 252 9 WITH with IN 20214 252 10 YOU you PRP 20214 252 11 , , , 20214 252 12 the the DT 20214 252 13 same same JJ 20214 252 14 as as IN 20214 252 15 you -PRON- PRP 20214 252 16 would would MD 20214 252 17 a a DT 20214 252 18 fountain fountain NN 20214 252 19 pen pen NN 20214 252 20 or or CC 20214 252 21 pencil pencil NN 20214 252 22 . . . 20214 253 1 The the DT 20214 253 2 present present JJ 20214 253 3 day day NN 20214 253 4 wonders wonder NNS 20214 253 5 of of IN 20214 253 6 the the DT 20214 253 7 twentieth twentieth JJ 20214 253 8 century century NN 20214 253 9 prove prove VBP 20214 253 10 that that IN 20214 253 11 there there EX 20214 253 12 is be VBZ 20214 253 13 no no DT 20214 253 14 end end NN 20214 253 15 to to IN 20214 253 16 what what WP 20214 253 17 an an DT 20214 253 18 individual individual NN 20214 253 19 can can MD 20214 253 20 accomplish accomplish VB 20214 253 21 -- -- : 20214 253 22 the the DT 20214 253 23 same same JJ 20214 253 24 applies apply VBZ 20214 253 25 to to IN 20214 253 26 the the DT 20214 253 27 slide slide NN 20214 253 28 rule rule NN 20214 253 29 . . . 20214 254 1 You -PRON- PRP 20214 254 2 will will MD 20214 254 3 find find VB 20214 254 4 after after IN 20214 254 5 practice practice NN 20214 254 6 that that IN 20214 254 7 you -PRON- PRP 20214 254 8 will will MD 20214 254 9 be be VB 20214 254 10 able able JJ 20214 254 11 to to TO 20214 254 12 do do VB 20214 254 13 many many JJ 20214 254 14 specialized specialized JJ 20214 254 15 problems problem NNS 20214 254 16 that that WDT 20214 254 17 are be VBP 20214 254 18 not not RB 20214 254 19 outlined outline VBN 20214 254 20 in in IN 20214 254 21 this this DT 20214 254 22 instruction instruction NN 20214 254 23 book book NN 20214 254 24 . . . 20214 255 1 It -PRON- PRP 20214 255 2 depends depend VBZ 20214 255 3 entirely entirely RB 20214 255 4 upon upon IN 20214 255 5 your -PRON- PRP$ 20214 255 6 ability ability NN 20214 255 7 to to TO 20214 255 8 do do VB 20214 255 9 what what WP 20214 255 10 we -PRON- PRP 20214 255 11 advocate advocate VBP 20214 255 12 and and CC 20214 255 13 to to TO 20214 255 14 be be VB 20214 255 15 slide slide NN 20214 255 16 - - HYPH 20214 255 17 rule rule NN 20214 255 18 conscious conscious JJ 20214 255 19 in in IN 20214 255 20 all all DT 20214 255 21 your -PRON- PRP$ 20214 255 22 mathematical mathematical JJ 20214 255 23 problems problem NNS 20214 255 24 . . . 20214 256 1 CONVERSION CONVERSION NNP 20214 256 2 FACTORS FACTORS NNP 20214 256 3 1 1 CD 20214 256 4 . . . 20214 257 1 Length length NN 20214 257 2 1 1 CD 20214 257 3 mile mile NN 20214 257 4 = = SYM 20214 257 5 5280 5280 CD 20214 257 6 feet foot NNS 20214 257 7 = = SYM 20214 257 8 1760 1760 CD 20214 257 9 yards yard NNS 20214 257 10 1 1 CD 20214 257 11 inch inch NN 20214 257 12 = = SYM 20214 257 13 2.54 2.54 CD 20214 257 14 centimeters centimeter NNS 20214 257 15 1 1 CD 20214 257 16 meter meter NN 20214 257 17 = = SYM 20214 257 18 39.37 39.37 CD 20214 257 19 inches inch NNS 20214 257 20 2 2 CD 20214 257 21 . . . 20214 258 1 Weight Weight NNP 20214 258 2 ( ( -LRB- 20214 258 3 or or CC 20214 258 4 Mass Mass NNP 20214 258 5 ) ) -RRB- 20214 258 6 1 1 CD 20214 258 7 pound pound NN 20214 258 8 = = SYM 20214 258 9 16 16 CD 20214 258 10 ounces ounce NNS 20214 258 11 = = SYM 20214 258 12 0.4536 0.4536 CD 20214 258 13 kilograms kilogram NNS 20214 258 14 1 1 CD 20214 258 15 kilogram kilogram NN 20214 258 16 = = SYM 20214 258 17 2.2 2.2 CD 20214 258 18 pounds pound NNS 20214 258 19 1 1 CD 20214 258 20 long long JJ 20214 258 21 ton ton NN 20214 258 22 = = SYM 20214 258 23 2240 2240 CD 20214 258 24 pounds pound NNS 20214 258 25 1 1 CD 20214 258 26 short short JJ 20214 258 27 ton=2000 ton=2000 CD 20214 258 28 pounds pound NNS 20214 258 29 3 3 CD 20214 258 30 . . . 20214 259 1 Volume volume NN 20214 259 2 1 1 CD 20214 259 3 liquid liquid JJ 20214 259 4 quart quart NN 20214 259 5 = = SYM 20214 259 6 0.945 0.945 CD 20214 259 7 litres litre NNS 20214 259 8 1 1 CD 20214 259 9 litre litre NN 20214 259 10 = = SYM 20214 259 11 1.06 1.06 CD 20214 259 12 liquid liquid JJ 20214 259 13 quarts quart NNS 20214 259 14 1 1 CD 20214 259 15 U. U. NNP 20214 259 16 S. S. NNP 20214 259 17 gallon gallon NN 20214 259 18 = = SYM 20214 259 19 4 4 CD 20214 259 20 quarts quart NNS 20214 259 21 = = SYM 20214 259 22 231 231 CD 20214 259 23 cubic cubic JJ 20214 259 24 inches inch NNS 20214 259 25 4 4 CD 20214 259 26 . . . 20214 260 1 Angular angular JJ 20214 260 2 Measure measure NN 20214 260 3 3.14 3.14 CD 20214 260 4 radians radians NNPS 20214 260 5 = = SYM 20214 260 6 PI pi NN 20214 260 7 radians radian NNS 20214 260 8 = = SYM 20214 260 9 180 180 CD 20214 260 10 degrees degree NNS 20214 260 11 1 1 CD 20214 260 12 radian radian JJ 20214 260 13 = = SYM 20214 260 14 57.30 57.30 CD 20214 260 15 degrees degree NNS 20214 260 16 5 5 CD 20214 260 17 . . . 20214 261 1 Pressure pressure NN 20214 261 2 760 760 CD 20214 261 3 millimeters millimeter NNS 20214 261 4 of of IN 20214 261 5 mercury mercury NN 20214 261 6 = = SYM 20214 261 7 14.7 14.7 CD 20214 261 8 pounds pound NNS 20214 261 9 per per IN 20214 261 10 square square JJ 20214 261 11 inch inch NN 20214 261 12 6 6 CD 20214 261 13 . . . 20214 262 1 Power power NN 20214 262 2 1 1 CD 20214 262 3 horse horse NN 20214 262 4 power power NN 20214 262 5 = = SYM 20214 262 6 550 550 CD 20214 262 7 foot foot NN 20214 262 8 pounds pound NNS 20214 262 9 per per IN 20214 262 10 second second JJ 20214 262 11 = = SYM 20214 262 12 746 746 CD 20214 262 13 watts watt NNS 20214 262 14 7 7 CD 20214 262 15 . . . 20214 263 1 Miscellaneous miscellaneous JJ 20214 263 2 60 60 CD 20214 263 3 miles mile NNS 20214 263 4 per per IN 20214 263 5 hour hour NN 20214 263 6 = = SYM 20214 263 7 88 88 CD 20214 263 8 feet foot NNS 20214 263 9 per per IN 20214 263 10 second second JJ 20214 263 11 980 980 CD 20214 263 12 centimeters centimeter NNS 20214 263 13 per per IN 20214 263 14 second second JJ 20214 263 15 per per IN 20214 263 16 second second JJ 20214 263 17 = = SYM 20214 263 18 32.2 32.2 CD 20214 263 19 feet foot NNS 20214 263 20 per per IN 20214 263 21 second second JJ 20214 263 22 per per IN 20214 263 23 second second NN 20214 263 24 = = SYM 20214 263 25 acceleration acceleration NN 20214 263 26 of of IN 20214 263 27 gravity gravity NN 20214 263 28 . . . 20214 264 1 1 1 CD 20214 264 2 cubic cubic JJ 20214 264 3 foot foot NN 20214 264 4 of of IN 20214 264 5 water water NN 20214 264 6 weighs weigh VBZ 20214 264 7 62.4 62.4 CD 20214 264 8 pounds pound NNS 20214 264 9 1 1 CD 20214 264 10 gallon gallon NN 20214 264 11 of of IN 20214 264 12 water water NN 20214 264 13 weighs weigh VBZ 20214 264 14 8.34 8.34 CD 20214 264 15 pounds pound NNS 20214 264 16 Printed Printed NNP 20214 264 17 in in IN 20214 264 18 U. U. NNP 20214 264 19 S. S. NNP 20214 264 20 A. a. NN 20214 265 1 INSTRUCTIONS INSTRUCTIONS NNP 20214 265 2 FOR for IN 20214 265 3 USING use VBG 20214 265 4 A a DT 20214 265 5 SLIDE SLIDE NNP 20214 265 6 RULE rule NN 20214 265 7 COPYRIGHTED copyright VBN 20214 265 8 BY by IN 20214 265 9 W. W. NNP 20214 265 10 STANLEY STANLEY NNP 20214 265 11 & & CC 20214 265 12 CO CO NNP 20214 265 13 . . . 20214 265 14 Commercial Commercial NNP 20214 265 15 Trust Trust NNP 20214 265 16 Building Building NNP 20214 265 17 , , , 20214 265 18 Philadelphia Philadelphia NNP 20214 265 19 , , , 20214 265 20 Pa. Pennsylvania NNP