answers to chapter 3 exercises - the first step to success · pdf file250 30. a. thirty and...
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249
Answers to Chapter 3 Exercises Exercise Set 3.1
1. 73
4 2. 6
7
8
3. !41
7 4. !4
1
12
5. 123
13 6. 17
2
11
7. !1413
15 8. !27
2
17
9. 21
4 10. 25
3
11. !19
2 12. !
53
6
13. 161
13 14. 161
11
15. !278
15 16. !
299
18
17. < 18. < 19. > 20. < 21. > 22. > 23. < 24. <
25. a. thirteen and twenty-five hundredths b. 10 + 3+ 2
10+5
100
26. a. fourteen and thirty-eight hundredths b. 10 + 4 + 3
10+8
100
27. a. nine and four hundred eight thousandths
b. 9 + 4
10+
8
1000
28. a. four and three hundred seven thousandths
b. 4 + 3
10+
7
1000
29. a. twenty-five and fifty-six thousandths b.20 + 5 + 5
100+
6
1000
250
30. a. thirty and forty-nine thousandths b. 30 + 4
100+
9
1000
31. a. six and five thousand six hundred eight ten-thousandths
b.6 + 5
10+6
100+
8
10000
32. a. five and nine thousand seven hundred two ten-thousandths
b. 5 + 9
10+7
100+
2
10000
33. a. twenty-three and eight thousand six hundred forty-seven ten-thousandths
b. 20 + 3+ 8
10+6
100+
4
1000+
7
10000
34. a. forty-two and seven thousand six hundred twenty-nine ten-thousandths
b. 40 + 2 + 7
10+6
100+
2
1000+
9
10000
35. 16 36. 23 37. 12.5 38. 15.3 39. 4.85 40. 6.75 41. 6.899 42. 6.900 43. 14.5490 44. 12.6600 45. tenths 46. tenths 47. hundredths 48. hundredths 49. hundredths 50. hundredths 51. ones 52. ones 53. thousandths 54. thousandths
55. 47
100 56. 93
100
57. !909
1000 58. !
851
1000
59. 239
10 60. 15 7
10
61. !15667
1000 62. !144
439
1000
63. 12 59
10000 64. 19 193
10000
65. 5.34 66. 9.72 67. 46.385 68. 88.219 69. 23.075 70. 65.807 71. 350.4069 72. 2009.7501 73. 0.28 74. 0.225
251
75. –0.2125 76. !0.106 77. 0.714285 78. 0.36 79. !0.54 80. !0.857142 81. 0.53 82. 0.86 83. 12.8 84. 15.35 85. –23.275 86. –16.2875 87. 5.6 88. 12.1 89. !13.83 90. !15.16 91. 26.384615 92. 32.692307 93. a. 27 b. 3 c. 0.185 94. a. 54 b. 4 c. 0.2407 95. a. 0.1 b. 0.2
c. 3
9= 0.3;
4
9= 0.4;
5
9= 0.5;
6
9= 0.6;
7
9= 0.7;
8
9= 0.8
d. 0.9 = 1; They are the same. 96. a. 0.13 b. 0.56 c. 0.78 d. 0.99 = 1 ; They are the same. Exercise Set 3.2 1. Equivalent 2. Equivalent 3. Not equivalent 4. Not equivalent 5. Equivalent 6. Equivalent 7. Equivalent 8. Equivalent 9. Not equivalent 10. Not equivalent
11. 12
26,!18
!39,6a
13a 12. 14
22,!21
!33,7xy
11xy
13. !15
36,!50
120,!5x
2
12x2
14. !16
30,!40
75,!8ab
15ab
15. !15x
25,!3xy
5y,!6x
2
10x 16. !
8a
14,!12ab
21b,!20a
2
35a
17. 12a
14b,18ab
21b2,!30a
2
!35ab 18. 10s
18t,25st
27t2,!15s
2
!27st
19. x = 40 20. x = 42 21. x = 280 22. x = 126 23. y = 255 24. y = 342
252
25. y = 240 26. y = 288 27. a = 5 28. a = 11 29. a = 11 30. a = 9 31. b = 11 32. b = 11 33. b = 17 34. b = 21
35. 3
5 36. 5
8
37. !14
15 38. !
8
21
39. 35
72 40. 49
93
41. !3
5 42. !
3
10
43. 5
11 44. 2
11
45. !3
5 46. !
28
39
47. 4y
5a 48. 5b
8x
49. !8b
15y 50. !
3x
5b
51. 2
3 52. 7
17
53. !9
10 54. !
5
9
55. 12
13 56. 10
11
57. !27
32 58. !
25
26
59. 27
64 60. 245
246
61. !5
8 62. !
9
16
63. 8
9 64. 7
9
65. !9
10 66. !
5
8
253
67. 3y2
x 68. 2y
3
x3
69. 4a2b4
3 70. 2a
2b2
3
71. !4y
5
5x 72. !
3y3
2x3
73. repeating 74. repeating 75. terminating 76. terminating 77. repeating 78. repeating 79. terminating 80. terminating 81. terminating 82. terminating 83. True 84. True 85. True 86. True
87. False ( 33= 0.9 = 1) 88. False ( 0.5 = 5
10=1
2)
Exercise Set 3.3
1. 2
3 2. 4
5
3. !3
8 4. !
1
4
5. –1 6. !1
7. !8
15 8. !
1
3
9. !3
4 10. !
3
8
11. !7
10 12. !
3
16
13. 3x ! 5y
14 14. 17a ! 9b
25
15. 3
2 16. 11
8
17. !3
16 18. !
3
20
19. !29
120 20. !
11
40
254
21. !1
6 22. 1
18
23. !7
12 24. !
5
12
25. !11
8 26. !
23
18
27. !23
24 28. !
19
14
29. !1
3 30. !
173
150
31. !13
20 32. !
7
8
33. 101
72 34. 253
288
35. !1
105 36. !
32
21
37. !29
24 38. !
289
200
39. 7
80 40. !
119
240
41. !41
90 42. !
79
105
43. !109
72 44. !
311
216
45. !1
24x 46. !
1
30x
47. 25b ! 32a
60ab 48. 9b !14a
24ab
49. 1316
50. 18 58
51. 2011
12 52. 24
53. !45
8 54. !5
1
6
55. !417
60 56. !5
23
60
255
57. !45
6 58. !4
7
12
59. !55
24 60. 1 23
24
61. !911
12 62. !13
9
40
63. !161
2 64. !14
3
4
65. 28.423 66. 32.366 67. 32.798 68. 32.356 69. 4.387 70. 46.666 71. 10.54 72. 15.15 73. 73.593 74. 49.251 75. –4.173 76. –8.126 77. –7.904 78. –21.73 79. –34.27 80. –44.419 81. $221.70 82. $493.72 83. $275.84 84. $879.22 85. $874.02 86. $632.38
87. 141 34
88. 487
16
89. 61
8inches 90. 9
3
8inches
Exercise Set 3.4
1. 1
6 2. 21
25
3. 2
5 4. 28
45
5. !7
15 6. !
7
20
7. !3
22 8. !
5
8
9. 10
21 10. 3
5
11. 1
7 12. 1
12
256
13. !3
7 14. !
2
7
15. 17
30 16. 8
63
17. 1
y 18. 2a
3y
19. 3ay
5b 20. 2x
a
21. 5
6 22. 15
2
23. !5
9 24. !
4
3
25. 10
33 26. 5
2
27. !1
2 28. !
7
8
29. !1
16 30. !
1
18
31. 2b
3ay 32. 3b
2x
33. 3xb2
4ay 34. 5a
6x
35. 662
3 36. 102 2
5
37. 217
20 38. 15
9
39. 63
4 40. !11
1
9
41. !69
80 42. 3
1
19
43. –30 44. –80
45. !17
10 46. !1
7
18
47. 10 12
48. 24
257
49. !71
2 50. !6
9
16
51. !13
4 52. !
4
5
53. 1 3132
54. 11956
55. 1.872 56. 5.46 57. –14.748 58. –30.483 59. –159.04 60. –128.832 61. 9.821 62. 148.915 63. 0.005683 64. 0.0437 65. –3.69 66. –52.5 67. 0.67 68. 0.642 69. –168.1 70. –241.05 71. –8.8 72. –3.3 73. 113.2 74. 1790 75. 47.06 76. 411.0416 77. 0.9568 78. 0.1035 79. 0.005683 80. 0.000237 81. 0.00468 82. 0.0000985
83. a. 18 r 3 b. 18 35
c. 18.6
84. a. 22 r 4 b. 22 45
c. 22.8
85. a. 30 r 3 b. 30 34
c. 30.75
86. a. 61 r 3 b. 61 34
c. 61.75
87. a. 53 r 9 b. 53 34
c. 53.75
88. a. 30 r 5 b. 30 13
c. 30.3
89. a. 72 r 1 b. 72 112
c. 72.083
90. a. 62 r 5 b. 62 511
c. 62.45
91. a. 26 r 2 b. 26 211
c. 26.18
258
92. a. 52 r 28 b. 52 28101
c. 52.2772
93. $14,613.60 94. $16,774.56 95. $2,957.24 96. $1,292.72 97. 36 pencils 98. 338 days
99. 339
10tons 100. 90 1
2tons
101. $937.50 102. $64,000 103. $132.50 104. $228.45 105. $77,076 106. $256,596 107. $1,936 108. $9,344 109. $1,725 loss 110. $2,760 gain
111. 3 5794
112. 4 819
113. 1001 114. 945 115. 160 116. 225 Exercise Set 3.5
1. 4
25 2. 16
49
3. !27
125 4. !
125
512
5. !16
25 6. !
25
36
7. 134
9 8. 27
9
16
9. !210
27 10. !15
5
8
11. 0.008 12. –0.027 13. 1.69 14. 1.21 15. –0.64 16. –1.44
17. 1
6 18. 27
100
19. 9
56 20. 10
27
21. 1
96 22. 5
243
259
23. 2x
y 24. 4
9
25. 9
16 26. 9b
20a
27. 7
24 28. 19
40
29. 5
14 30. 9
22
31. !1
12 32. !
1
26
33. 4
15 34. 1
8
35. 5
16 36. 5
36
37. 13
75 38. 17
24
39. !1
8 40. 5
16
41. 7
45 42. !
5
144
43. 53
192 44. 197
300
45. 41
144 46. 53
144
47. !611
12 48. !11
7
24
49. !319
24 50. !3
19
24
51. 12 4360
52. 813
40
53. 244
15 54. 15 27
40
55. 419
24 56. 119
20
57. !965
72 58. !20
5
8
260
59. 35
24 60. 2
5
8
61. 111316
62. 279
120
63. 45
16 64. 5
113
144
65. !2429
36 66. !19
11
16
67. 9
10 68. 3
2
69. 9
8 70. 4
3
71. 39
8 72. 15
2
73. 51
10 74. 34
7
75. 17
44 76. 3
5
77. 5
16 78. 20
3
79. !14
53 80. !
76
129
81. –2 82. !25
7
83. 31
6 84. 4
1
3
85. 52
15 86. 6
59
72
87. !123
36 88. !1
9
20
89. 3
16 90. !2
7
16
91. 5.1275 92. 7.8825 93. –1.4525 94. –3.9775 95. 6.28 96. 8.55 97. –7.34 98. –15.33 99. 21.96 100. 13.26
261
101. 1.81 102. 5.24 103. –22.88 104. –15.18 105. 1.44 106. 2.89 107. –7.02 108. 14.96 109. 16.32 110. 7.82 111. –30.41 112. –28.84 113. 4.95 114. 4.68 Exercise Set 3.6 1. > 2. < 3. < 4. < 5. < 6. < 7. < 8. > 9. > 10. > 11. < 12. > 13. > 14. > 15.
16.
17.
18.
19.
20.
21.
22.
23.
262
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37. Yes 38. No 39. No 40. Yes 41. Yes 42. No 43. No 44. Yes 45. No 46. Yes 47. Yes 48. No 49. No 50. Yes
263
51. Yes 52. No
53. geometric; ratio = 12
, next term = ! 112
54. geometric; ratio = 13
, next term = ! 136
55. geometric; ratio = 12
, next term =!1
2
56. geometric; ratio = 13
, next term = ! 13
57. arithmetic; difference =!2
3, next term = –1
58. arithmetic; difference = 34
, next term = 54
59. arithmetic; difference =!3
2, next term = ! 5
2
60. arithmetic; difference =!2
3, next term = –1
61. geometric; ratio =!1
2, next term = 3
2
62. geometric; ratio =!1
3, next term = ! 4
9
63. geometric; ratio =!2
3, next term = 10
81
64. geometric; ratio =!2
3, next term = ! 4
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
264
Exercise Set 3.7 1. 2.3!10
4 2. 5.7 !104
3. 1.44 !105 4. 2.56 !10
5 5. !1.24 "10
6 6. !5.89 "106
7. !8 "108 8. !9 "10
9 9. 5.7205 !10
7 10. 4.932 !107
11. !1.32 "102 12. !4.8 "10
1 13. !8 "10
0 14. 6 !100
15. 8 !10"3 16. 7 !10
"3 17. 4.56 !10
"2 18. 2.86 !10"2
19. !7.5 "10!1 20. !8.4 "10
!1 21. !4.05 "10
!5 22. !3.04 "10!5
23. 5.0 !10"4 24. 6.00 !10
"5 25. 7 !10
"1 26. 9.9 !10"1
27. !2.05 "100 28. !5.804 "10
0 29. 4.0000 !10
"2 30. 5.000 !10"3
31. 38,600 32. 547,000 33. 309 34. 5,070,000 35. –5,800 36. –84,000 37. –20,030 38. –900,700 39. 400,500,000 40. 3,009,000,000 41. 0.0058 42. 0.063 43. –0.000385 44. –0.0000906 45. 0.000060 46. 0.000000070 47. 0.0006004 48. 0.009035 49. –0.0008000 50. –0.0000600 51. two 52. two 53. two 54. three 55. four 56. five 57. five 58. six 59. four 60. three 61. three 62. three 63. four 64. six 65. three 66. four 67. a. 9.3!10
7 b. two 68. a. 1.86 !10
5 b. three 69. a. 5.2 !10
"4 b. two
265
70. a. 5.9 !1012 b. two
71. 94,000,000,000 = 9.4 !1010 72. 104,000,000,000 = 1.04 !1011
73. a. 3.4 !107 b. two c. 1.7952 !10
11 74. a. 4.66 !10
8 b. three c. 2.46048 !1012
75. 5.6 !107 76. 4.25 !10
7 77. 2.6 !10
"3 78. 4.3!10"2
79. 4.5 !105 80. 3!10
3 81. 5.32 !10
"5 82. 8.5 !10"7
Chapter 3 Review Exercises
1. 85
7 2. 11
2
13
3. !57
9 4. !17
4
5
5. 188
13 6. 79
5
7. !89
9 8. !
194
13
9. > 10. > 11. < 12. > 13. a. five and eight hundred nine thousandths
b. 5 + 8
10+
9
1000
14. a. twelve and eighty-two hundredths
b. 10 + 2 + 8
10+2
100
15. a. five and thirty-eight ten-thousandths
b. 5 + 3
1000+
8
10000
16. a. twenty-three and four thousand five hundred eighty-one ten-thousandths
b. 20 + 3+ 4
10+5
100+
8
1000+
1
10000
17. 105 18. 17.7 19. 15.50 20. 8.594 21. tenths 22. hundredths 23. hundredths 24. thousandths
266
25. 49
10 26. 51
100
27. !97
100 28. !6
517
1000
29. 86.039 30. 57.405 31. –0.52 32. –0.425 33. 0.83 34. 0.73 35. –26.625 36. !12.571428 37. Equivalent 38. Not equivalent 39. Not equivalent 40. Not equivalent
41. !24
34,!36
51,!12ax
17ax 42. 10a
14b,!15a
!21b,5a
2
7ab
43. x = 72 44. y = !156 45. a = 3 46. b = 9
47. 5
9 48. !
3
4
49. !3a
7b 50. 3b
7y
51. 3
5 52. 5
37
53. !3
11 54. !
5y2
4x3
55. 3
5 56. !
1
6
57. !17
24 58. !
77
90
59. !71
720 60. !
73
180
61. 251
4 62. 4
13
24
63. !1416
45 64. !3
7
12
65. 22.636 66. 22.368 67. –6.131 68. –41.532
69. !25
48 70. 3
5
267
71. 1
3 72. 9x
20b
73. 7
12 74. !
1
12
75. 3b
2ay 76. 3by
2ax
77. –12 78. 44
7
79. 7
12 80. 6
81. 1.225 82. –55.08 83. –0.237 84. 0.076 85. 0.7625 86. –0.65 87. 0.12867 88. 19.416
89. a. 108 r 3 b. 108 34
c. 108.75
90. a. 45 r 10 b. 45 23
c. 45.6
91. 49
4 92. 1.44
93. 33
4 94. 9
16
95. 3
14 96. !
2
27
97. !7
48 98. !
23
72
99. !77
12 100. 20 1
3
101. !6 2930
102. !11 41144
103. 3310
104. 726
105. ! 1776
106. !4 113
107. 389
108. !2 320
109. 4.8225 110. –3.47
268
111. –30.17 112. –41.95 113. –49.99 114. 3.6 115. < 116. > 117. > 118. > 119.
120.
121.
122.
123. No 124. Yes 125. Yes 126. No
127. arithmetic; difference = 14
, next term = 0
128. arithmetic; difference = –1.1, next term = – 4.5
129. geometric; ratio =!1
4, next term = ! 3
16
130. geometric; ratio = –0.2, next term = –0.072 131. 5.07 !105 132. !2.45 "106 133. !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
145. 110 916
146. $17,860.80
147. 285 days 148. $145,000 149. Net gain of $162.19 (rounded) 150. $245,693.20