Idea Transcript
Answers to Chapter 3 Exercises Exercise Set 3.1 1. 3. 5. 7. 9. 11. 13. 15. 17. 19. 21. 23.
3 4 1 !4 7 3 12 13 13 !14 15 21 4 19 ! 2 161 13 278 ! 15 < > > <
2.
7
25. a. 26. a. 27. a. b. 28. a. b. 29. a.
6
7 8
1 12 2 6. 17 11 2 8. !27 17 25 10. 3 53 12. ! 6 161 14. 11 299 16. ! 18 18. < 20. < 22. > 24. < 2 5 thirteen and twenty-five hundredths b. 10 + 3 + + 10 100 3 8 fourteen and thirty-eight hundredths b. 10 + 4 + + 10 100 nine and four hundred eight thousandths 4 8 9+ + 10 1000 four and three hundred seven thousandths 3 7 4+ + 10 1000 5 6 twenty-five and fifty-six thousandths b. 20 + 5 + + 100 1000
4.
249
!4
4 9 + 100 1000 a. six and five thousand six hundred eight ten-thousandths 5 6 8 b. 6 + + + 10 100 10000 a. five and nine thousand seven hundred two ten-thousandths 9 7 2 b. 5 + + + 10 100 10000 a. twenty-three and eight thousand six hundred forty-seven ten-thousandths 8 6 4 7 b. 20 + 3 + + + + 10 100 1000 10000 a. forty-two and seven thousand six hundred twenty-nine ten-thousandths 7 6 2 9 b. 40 + 2 + + + + 10 100 1000 10000 16 36. 23 12.5 38. 15.3 4.85 40. 6.75 6.899 42. 6.900 14.5490 44. 12.6600 tenths 46. tenths hundredths 48. hundredths hundredths 50. hundredths ones 52. ones thousandths 54. thousandths 47 93 56. 100 100 909 851 58. ! ! 1000 1000 9 7 60. 15 23 10 10 667 439 62. !144 !15 1000 1000 59 193 64. 19 12 10000 10000 5.34 66. 9.72 46.385 68. 88.219 23.075 70. 65.807 350.4069 72. 2009.7501 0.28 74. 0.225
30. a. thirty and forty-nine thousandths 31.
32.
33.
34.
35. 37. 39. 41. 43. 45. 47. 49. 51. 53. 55. 57. 59. 61. 63. 65. 67. 69. 71. 73.
250
b. 30 +
75. 77. 79. 81. 83. 85. 87. 89. 91. 93. 94. 95.
–0.2125 0.714285 !0.54 0.53 12.8 –23.275 5.6 !13.83 26.384615 a. 27 b. 3 a. 54 b. 4 a. 0. 1 b. 0.2 3 4 5 6 7 c. = 0.3; = 0.4; = 0.5; = 0.6; 9 9 9 9 9 d. 0.9 = 1 ; They are the same. 96. a. 0.13 b. 0.56 d. 0.99 = 1 ; They are the same.
76. 78. 80. 82. 84. 86. 88. 90. 92. c. c.
!0.106 0.36 !0.857142 0.86 15.35 –16.2875 12. 1 !15.16 32.692307 0.185 0.2407
= 0.7;
8 = 0.8 9
c.
0.78
2. 4. 6. 8. 10.
Equivalent Not equivalent Equivalent Equivalent Not equivalent 14 !21 7xy , , 22 !33 11xy 16 40 8ab ! ,! ,! 30 75 15ab 8a 12ab 20a 2 ! ,! ,! 14 21b 35a 2 10s 25st !15s , , 18t 27t 2 !27st x = 42 x = 126 y = 342
Exercise Set 3.2 1. 3. 5. 7. 9. 11. 13. 15. 17. 19. 21. 23.
Equivalent Not equivalent Equivalent Equivalent Not equivalent 12 !18 6a , , 26 !39 13a 15 50 5x 2 ! ,! ,! 36 120 12x 2 15x 3xy 6x 2 ! ,! ,! 25 5y 10x 12a 18ab !30a 2 , , 14b 21b 2 !35ab x = 40 x = 280 y = 255
12. 14. 16. 18. 20. 22. 24.
251
25. 27. 29. 31. 33. 35. 37. 39. 41. 43. 45. 47. 49. 51. 53. 55. 57. 59. 61. 63. 65.
y = 240 a=5 a = 11 b = 11 b = 17 3 5 14 ! 15 35 72 3 ! 5 5 11 3 ! 5 4y 5a 8b ! 15y 2 3 9 ! 10 12 13 27 ! 32 27 64 5 ! 8 8 9 9 ! 10
26. 28. 30. 32. 34. 36. 38. 40. 42. 44. 46. 48. 50. 52. 54. 56. 58. 60. 62. 64. 66.
252
y = 288 a = 11 a=9 b = 11 b = 21 5 8 8 ! 21 49 93 3 ! 10 2 11 28 ! 39 5b 8x 3x ! 5b 7 17 5 ! 9 10 11 25 ! 26 245 246 9 ! 16 7 9 5 ! 8
67. 69. 71. 73. 75. 77. 79. 81. 83. 85. 87.
3y 2 x 4a 2b 4 3 4y 5 ! 5x repeating terminating repeating terminating terminating True True 3 False ( = 0.9 = 1 ) 3
68. 70. 72. 74. 76. 78. 80. 82. 84. 86.
2y 3 x3 2a 2b 2 3 3y 3 ! 3 2x repeating terminating repeating terminating terminating True True
88. False ( 0.5 =
Exercise Set 3.3 1. 3. 5. 7. 9. 11. 13. 15. 17. 19.
2 3
2.
3 8 –1 8 ! 15 3 ! 4 7 ! 10 3x ! 5y 14 3 2 3 ! 16 29 ! 120 !
4. 6. 8. 10. 12. 14. 16. 18. 20.
253
4 5 1 4 !1 1 ! 3 3 ! 8 3 ! 16 17a ! 9b 25 11 8 3 ! 20 11 ! 40 !
5 1 = ) 10 2
1 6 7 ! 12 11 ! 8 23 ! 24 1 ! 3 13 ! 20 101 72 1 ! 105 29 ! 24 7 80 41 ! 90 109 ! 72 1 ! 24x 25b ! 32a 60ab 1 13 6 11 20 12 5 !4 8 17 !4 60
21. !
22.
23.
24.
25. 27. 29. 31. 33. 35. 37. 39. 41. 43. 45. 47. 49. 51. 53. 55.
26. 28. 30. 32. 34. 36. 38. 40. 42. 44. 46. 48. 50.
1 18 5 ! 12 23 ! 18 19 ! 14 173 ! 150 7 ! 8 253 288 32 ! 21 289 ! 200 119 ! 240 79 ! 105 311 ! 216 1 ! 30x 9b ! 14a 24ab 5 18 8
52. 24 1 6 23 56. !5 60
54. !5
254
5 6 5 !5 24 11 !9 12 1 !16 2 28.423 32.798 4.387 10.54 73.593 –4.173 –7.904 –34.27 $221.70 $275.84 $874.02 3 141 4 1 6 inches 8
7 12 23 1 24 9 !13 40 3 !14 4 32.366 32.356 46.666 15.15 49.251 –8.126 –21.73 –44.419 $493.72 $879.22 $632.38 7 48 16 3 9 inches 8
57. !4
58. !4
59.
60.
61. 63. 65. 67. 69. 71. 73. 75. 77. 79. 81. 83. 85. 87. 89.
62. 64. 66. 68. 70. 72. 74. 76. 78. 80. 82. 84. 86. 88. 90.
Exercise Set 3.4 1. 3.
1 6 2 5
21 25 28 4. 45 7 6. ! 20 5 8. ! 8 3 10. 5 1 12. 12
2.
7 15 3 7. ! 22 10 9. 21 1 11. 7
5.
!
255
3 7 17 30 1 y 3ay 5b 5 6 5 ! 9 10 33 1 ! 2 1 ! 16 2b 3ay 3xb 2 4ay 2 66 3 17 2 20 3 6 4 69 ! 80 –30 7 !1 10 1 10 2
2 7 8 63 2a 3y 2x a 15 2 4 ! 3 5 2 7 ! 8 1 ! 18 3b 2x 5a 6x 2 102 5 5 1 9 1 !11 9 1 3 19 –80 7 !1 18
13. !
14. !
15.
16.
17. 19. 21. 23. 25. 27. 29. 31. 33. 35. 37. 39. 41. 43. 45. 47.
18. 20. 22. 24. 26. 28. 30. 32. 34. 36. 38. 40. 42. 44. 46.
48. 24
256
1 2 3 !1 4 31 1 32 1.872 –14.748 –159.04 9.821 0.005683 –3.69 0.67 –168.1 –8.8 113.2 47.06 0.9568 0.005683 0.00468
9 16 4 ! 5 19 1 56 5.46 –30.483 –128.832 148.915 0.0437 –52.5 0.642 –241.05 –3.3 1790 411.0416 0.1035 0.000237 0.0000985
49. !7
50. !6
51.
52.
53. 55. 57. 59. 61. 63. 65. 67. 69. 71. 73. 75. 77. 79. 81.
54. 56. 58. 60. 62. 64. 66. 68. 70. 72. 74. 76. 78. 80. 82. 3 5 4 22 5 3 30 4 3 61 4 3 53 4 1 30 3 1 72 12 5 62 11 2 26 11
83. a. 18 r 3
b. 18
c. 18.6
84. a. 22 r 4
b.
c. 22.8
85. a. 30 r 3
b.
86. a. 61 r 3
b.
87. a. 53 r 9
b.
88. a. 30 r 5
b.
89. a. 72 r 1
b.
90. a. 62 r 5
b.
91. a. 26 r 2
b.
c. 30.75 c. 61.75 c. 53.75 c. 30.3 c. 72.083 c. 62.45 c. 26.18
257
92. a. 52 r 28
b. 52
28 101
c. 52.2772
93. $14,613.60 95. $2,957.24 97. 36 pencils 9 99. 33 tons 10 101. $937.50 103. $132.50 105. $77,076 107. $1,936 109. $1,725 loss 57 111. 3 94 113. 1001 115. 160
94. $16,774.56 96. $1,292.72 98. 338 days 1 100. 90 tons 2 102. $64,000 104. $228.45 106. $256,596 108. $9,344 110. $2,760 gain 8 112. 4 19 114. 945 116. 225
Exercise Set 3.5 1. 3. 5. 7. 9. 11. 13. 15. 17. 19. 21.
4 25 27 ! 125 16 ! 25 4 13 9 10 !2 27 0.008 1.69 –0.64 1 6 9 56 1 96
2. 4. 6. 8. 10. 12. 14. 16. 18. 20. 22.
258
16 49 125 ! 512 25 ! 36 9 27 16 5 !15 8 –0.027 1.21 –1.44 27 100 10 27 5 243
23. 25. 27. 29. 31. 33. 35. 37. 39. 41. 43. 45. 47. 49. 51. 53. 55. 57.
2x y 9 16 7 24 5 14 1 ! 12 4 15 5 16 13 75 1 ! 8 7 45 53 192 41 144 11 !6 12 19 !3 24 43 12 60 4 24 15 19 4 24 65 !9 72
24. 26. 28. 30. 32. 34. 36. 38. 40. 42. 44. 46. 48. 50. 52. 54. 56. 58.
259
4 9 9b 20a 19 40 9 22 1 ! 26 1 8 5 36 17 24 5 16 5 ! 144 197 300 53 144 7 !11 24 19 !3 24 13 8 40 27 15 40 19 1 20 5 !20 8
5 24 13 11 16 5 4 16 29 !24 36 9 10 9 8 39 8 51 10 17 44 5 16 14 ! 53
5 8 79 2 120 113 5 144 11 !19 16 3 2 4 3 15 2 34 7 3 5 20 3 76 ! 129 25 ! 7 1 4 3 59 6 72 9 !1 20 7 !2 16 7.8825 –3.9775 8.55 –15.33 13.26
59. 3
60. 2
61.
62.
63. 65. 67. 69. 71. 73. 75. 77. 79.
64. 66. 68. 70. 72. 74. 76. 78. 80.
81. –2
82.
1 6 2 5 15 23 !1 36 3 16 5.1275 –1.4525 6.28 –7.34 21.96
83. 3
84.
85.
86.
87. 89. 91. 93. 95. 97. 99.
88. 90. 92. 94. 96. 98. 100.
260
101. 103. 105. 107. 109. 111. 113.
1.81 –22.88 1.44 –7.02 16.32 –30.41 4.95
102. 104. 106. 108. 110. 112. 114.
5.24 –15.18 2.89 14.96 7.82 –28.84 4.68
2. 4. 6. 8. 10. 12. 14.
< < < > > > >
Exercise Set 3.6 1. 3. 5. 7. 9. 11. 13. 15.
> < < < > < >
16. 17. 18. 19. 20. 21. 22. 23.
261
24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 39. 41. 43. 45. 47. 49.
Yes No Yes No No Yes No
38. 40. 42. 44. 46. 48. 50.
262
No Yes No Yes Yes No Yes
51. Yes
52. No
1 1 53. geometric; ratio = , next term = ! 2 12 1 1 54. geometric; ratio = , next term = ! 3 36 1 1 55. geometric; ratio = , next term = ! 2 2 1 1 56. geometric; ratio = , next term = ! 3 3 2 57. arithmetic; difference = ! , next term = –1 3 3 5 58. arithmetic; difference = , next term = 4 4 3 5 59. arithmetic; difference = ! , next term = ! 2 2 2 60. arithmetic; difference = ! , next term = –1 3 1 3 61. geometric; ratio = ! , next term = 2 2 1 4 62. geometric; ratio = ! , next term = ! 3 9 2 10 63. geometric; ratio = ! , next term = 3 81 2 4 64. geometric; ratio = ! , next term = ! 3 21 65. arithmetic; difference = 0.4, next term = –0.6 66. arithmetic; difference = 1.1, next term = –0.1 67. arithmetic; difference = –0.9, next term = –1.2 68. arithmetic; difference = –1.4, next term = –1.9 69. geometric; ratio = –0.2, next term = –0.064 70. geometric; ratio = –0.3, next term = 0.135 71. Gain of $637.50. 72. Gain of $207.50. 73. $13,815.92 74. $39,330.56 75. $246,548.20 76. $270,503.60 77. $230,480 78. Decrease by $6536. 79. $2720.64 80. $1170.40 81. $1283.75 82. $18.50 more
263
Exercise Set 3.7 1. 3. 5. 7. 9. 11. 13. 15. 17. 19. 21. 23. 25. 27. 29. 31. 33. 35. 37. 39. 41. 43. 45. 47. 49. 51. 53. 55. 57. 59. 61. 63. 65. 67. 68. 69.
2.3 ! 10 4 1.44 ! 10 5 !1.24 " 10 6 !8 " 10 8 5.7205 ! 10 7 !1.32 " 10 2 !8 " 10 0 8 ! 10 "3 4.56 ! 10 "2 !7.5 " 10 !1 !4.05 " 10 !5 5.0 ! 10 "4 7 ! 10 "1 !2.05 " 10 0 4.0000 ! 10 "2 38,600 309 –5,800 –20,030 400,500,000 0.0058 –0.000385 0.000060 0.0006004 –0.0008000 two two four five four three four three a. 9.3 ! 10 7 a. 1.86 ! 10 5 a. 5.2 ! 10 "4
2. 4. 6. 8. 10. 12. 14. 16. 18. 20. 22. 24. 26. 28. 30. 32. 34. 36. 38. 40. 42. 44. 46. 48. 50. 52. 54. 56. 58. 60. 62. 64. 66. b. b. b.
264
5.7 ! 10 4 2.56 ! 10 5 !5.89 " 10 6 !9 " 10 9 4.932 ! 10 7 !4.8 " 101 6 ! 10 0 7 ! 10 "3 2.86 ! 10 "2 !8.4 " 10 !1 !3.04 " 10 !5 6.00 ! 10 "5 9.9 ! 10 "1 !5.804 " 10 0 5.000 ! 10 "3 547,000 5,070,000 –84,000 –900,700 3,009,000,000 0.063 –0.0000906 0.000000070 0.009035 –0.0000600 two three five six three three six four two three two
70. 71. 73. 74. 75. 77. 79. 81.
a. 5.9 ! 1012 94, 000, 000, 000 = 9.4 ! 1010 3.4 ! 10 7 a. b. two 8 4.66 ! 10 a. b. three 7 5.6 ! 10 2.6 ! 10 "3 4.5 ! 10 5 5.32 ! 10 "5
b. 72. c. c. 76. 78. 80. 82.
two 104, 000, 000, 000 = 1.04 ! 1011 1.7952 ! 1011 2.46048 ! 1012 4.25 ! 10 7 4.3 ! 10 "2 3 ! 10 3 8.5 ! 10 "7
Chapter 3 Review Exercises 1. 3. 5. 7. 9. 11. 13.
14.
15.
16.
17. 19. 21. 23.
2 13 7 4 4. !17 !5 9 5 188 79 6. 13 5 89 194 8. ! ! 9 13 > 10. > < 12. > a. five and eight hundred nine thousandths 8 9 b. 5 + + 10 1000 a. twelve and eighty-two hundredths 8 2 b. 10 + 2 + + 10 100 a. five and thirty-eight ten-thousandths 3 8 b. 5 + + 1000 10000 a. twenty-three and four thousand five hundred eighty-one ten-thousandths 4 5 8 1 b. 20 + 3 + + + + 10 100 1000 10000 105 18. 17.7 15.50 20. 8.594 tenths 22. hundredths hundredths 24. thousandths 8
5 7
2.
265
11
9 10 97 ! 100 86.039 –0.52 0.83 –26.625 Equivalent Not equivalent 24 36 12ax ! ,! ,! 34 51 17ax x = 72 a=3 5 9 3a ! 7b 3 5 3 ! 11 3 5 17 ! 24 71 ! 720 1 25 4 16 !14 45 22.636 –6.131 25 ! 48
25. 4
26.
27.
28.
29. 31. 33. 35. 37. 39. 41. 43. 45. 47. 49. 51. 53. 55. 57. 59. 61. 63. 65. 67. 69.
30. 32. 34. 36. 38. 40. 42. 44. 46. 48. 50. 52. 54. 56. 58. 60. 62. 64. 66. 68. 70.
266
51 100 517 !6 1000 57.405 –0.425 0.73 !12.571428 Not equivalent Not equivalent 10a !15a 5a 2 , , 14b !21b 7ab y = !156 b=9 3 ! 4 3b 7y 5 37 5y 2 ! 3 4x 1 ! 6 77 ! 90 73 ! 180 13 4 24 7 !3 12 22.368 –41.532 3 5
1 3 7 73. 12 3b 75. 2ay
9x 20b 1 74. ! 12 3by 76. 2ax 4 78. 4 7
71.
72.
77. –12 79. 81. 83. 85. 87.
7 12 1.225 –0.237 0.7625 0.12867
89. a. 108 r 3 90. a. 45 r 10 91. 93. 95. 97. 99. 101. 103. 105. 107. 109.
80. 6 82. 84. 86. 88. 3 4 2 b. 45 3
b. 108
–55.08 0.076 –0.65 19.416
c. 108.75 c. 45.6
49 4 33 4 3 14 7 ! 48 7 !7 12 29 !6 30 33 10 17 ! 76 8 3 9 4.8225
92. 1.44 94.
9 16
2 27 23 98. ! 72 1 100. 20 3
96. !
102. !11 104.
41 144
7 26
1 13 3 108. !2 20 110. –3.47
106. !4
267
111. 113. 115. 117. 119.
–30.17 –49.99 < >
112. 114. 116. 118.
–41.95 3.6 > >
120. 121. 122. 123. No 125. Yes
124. Yes 126. No
1 127. arithmetic; difference = , next term = 0 4 128. arithmetic; difference = –1.1, next term = – 4.5 1 3 129. geometric; ratio = ! , next term = ! 4 16 130. geometric; ratio = –0.2, next term = –0.072 131. 5.07 ! 10 5 132. !2.45 " 10 6 133. !5.04 " 10 !6 134. 6.50 ! 10 "5 135. –39,000 136. 5,080,000 137. 0.0006002 138. –0.000003304 139. two 140. three 141. three 142. four 143. $101.45 144. $723.33 9 145. 110 146. $17,860.80 16 147. 285 days 148. $145,000 149. Net gain of $162.19 (rounded) 150. $245,693.20
268