Chapter 5 5 Section 5.1 ... FIRST STATE BANK OF FARTHINGTON FARTHINGTON, IL 64422 ... 7. 167.009 in words is one hundred sixty-seven and nine thousandths

224

Chapter 5

Section 5.1

Practice Problems

1. a. 0.06 in words is six hundredths.

b. −200.073 in words is negative two hundred and seventy-three thousandths.

c. 0.0829 in words in eight hundred twenty-nine ten-thousandths.

2. 87.31 in words is eighty-seven and thirty-one hundredths.

3. 52.1085 in words is fifty-two and one thousand eighty-five ten thousandths.

4. The check should be paid to “CLECO,” for the amount of “207.40,” which is written in words

as “Two hundred seven and 40

100.”

FIRST STATE BANKO F F A R T H I N G T O N

FARTHINGTON, IL 64422

PAY TOTHE ORDER OF

DATE

MEMO

DOLLARS

$

60–8124/72331000613331

14 0 5

Two hundred seven and

CLECO

(Your signature)

Current date( (

207.4040

100/

Your Preprinted NameYour Preprinted Address

5. Five hundred and ninety-six hundredths is 500.96.

6. Thirty-nine and forty-two thousandths is 39.042.

7. 510.051

1000=

8. 9729.97 29

100=

9. 12 30.12100 25

= =

10. 8 464.8 64 64

10 5= =

11. 986 493209.986 209 209

1000 500− = − = −

12. 29.208 26.28 ↑ ↑ 0 < 8 so 26.208 < 26.28

13. 0.12 0.026 ↑ ↑ 1 > 0 so 0.12 > 0.026

14. 0.039 0.0309 ↑ ↑ 9 > 0 so 0.039 > 0.0309 Thus, −0.039 < −0.0309.

15. To round 482.7817 to the nearest thousandth, observe that the digit in the ten-thousandths place is 7. Since this digit is at least 5, we add 1 to the digit in the thousandths place. The number 482.7817 rounded to the nearest thousandth is 482.782.

16. To round −0.032 to the nearest hundredth, observe that the digit in the thousandths place is 2. Since this digit is less than 5, we do not add 1 to the digit in the hundredths place. The number −0.032 rounded to the nearest hundredth is −0.03.

17. To round 3.14159265 to the nearest ten-thousandth, observe that the digit in the hundred-thousandths place is 9. Since this digit is at least 5, we add 1 to the digit in the ten-thousandths place. The number 3.14159265 rounded to the nearest the ten-thousandth is 3.1416, or π ≈ 3.1416.

18. $24.62 rounded to the nearest dollar is $24, since 6 ≥ 5.

Vocabulary and Readiness Check

1. The number “twenty and eight hundredths” is written in words and “20.08” is written in standard form.

2. Another name for the distance around a circle is its circumference.

3. Like fractions, decimals are used to denote part of a whole.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Prentice Hall

ISM: Prealgebra Chapter 5: Decimals

225

4. When writing a decimal number in words, the decimal point is written as and.

5. The place value tenths is to the right of the decimal point while tens is to the left of the decimal point.

6. The decimal point in a whole number is after the last digit.

Exercise Set 5.1

1. 5.62 in words is five and sixty-two hundredths.

2. 9.57 in words is nine and fifty-seven hundredths.

3. 16.23 in words is sixteen and twenty-three hundredths.

4. 47.65 in words is forty-seven and sixty-five hundredths.

5. −0.205 in words is negative two hundred five thousandths.

6. −0.495 in words is negative four hundred ninety-five thousandths.

7. 167.009 in words is one hundred sixty-seven and nine thousandths.

8. 233.056 in words is two hundred thirty-three and fifty-six thousandths.

9. 3000.04 in words is three thousand and four hundredths.

10. 5000.02 in words is five thousand and two hundredths.

11. 105.6 in words is one hundred five and six tenths.

12. 410.3 in words is four hundred ten and three tenths.

13. 2.43 in words is two and forty-three hundredths.

14. 31.04 in words is thirty-one and four hundredths.

15. The check should be paid to “R.W. Financial,” for the amount “321.42,” which is written in words as “Three

hundred twenty-one and 42

100.”



PAY TOTHE ORDER OF


DATE

MEMO

DOLLARS

$

60–8124/72331000613331

14 0 7

R.W. FinancialThree hundred twenty-one and

Your signature

Current date( (

( (

321.4242100

/


Chapter 5: Decimals ISM: Prealgebra

226

16. The check should be paid to “Amanda Dupre,” for the amount “213.70,” which is written in words as “Two

hundred thirteen and 70

100.”



PAY TOTHE ORDER OF


DATE

MEMO

DOLLARS

$

60–8124/72331000613331

14 0 8

Two hundred thirteen and

Your signature

Current date( (

( (

213.7070100

/Amanda Dupre

17. The check should be paid to “Bell South,” for the amount of “59.68,” which is written in words as “Fifty-nine and 68 .

100”



PAY TOTHE ORDER OF


DATE

MEMO

DOLLARS

$

60–8124/72331000613331

14 0 9

Fifty-nine and

Your signature

Current date( (

( (

59.6868100

/Bell South

18. The check should be paid to “Albertsons,” for the amount of “87.49,” which is written in words as “Eighty-seven

and 49

100.”



PAY TOTHE ORDER OF


DATE

MEMO

DOLLARS

$

60–8124/72331000613331

14 1 0

Eighty -seven and

Your signature

Current date( (

( (

87.4949100

/Albertsons

19. Two and eight tenths is 2.8.

20. Five and one tenth is 5.1.

21. Nine and eight hundredths is 9.08.

22. Twelve and six hundredths is 12.06.

23. Negative seven hundred five and six hundred twenty-five thousandths is −705.625.

24. Negative eight-hundred four and three hundred ninety-nine thousandths is −804.399.

25. Forty-six ten-thousandths is 0.0046.

26. Eighty-three ten-thousandths is 0.0083.



227

27. 70.7

10=

28. 90.9

10=

29. 270.27

100=

30. 390.39

100=

31. 4 20.4

10 5= =

32. 8 40.8

10 5= =

33. 4 25.4 5 5

10 5= =

34. 8 46.8 6 6

10 5= =

35. 58 290.058

1000 500− = − = −

36. 24 30.024

1000 125− = − = −

37. 8 17.008 7 7

1000 125= =

38. 5 19.005 9 9

1000 200= =

39. 802 40115.802 15 15

1000 500= =

40. 406 20311.406 11 11

1000 500= =

41. 3005 6010.3005

10,000 2000= =

42. 2006 10030.2006

10,000 5000= =

43. Eight tenths is 0.8 and as a fraction is 8 4 .

10 5=

44. Five tenths is 0.5 and as a fraction is 5 1 .

10 2=

45. In words, 0.077 is seventy-seven thousandths.

As a fraction, 770.077 .

1000=

46. In words, 0.019 is nineteen thousandths. As a

fraction, 190.019 .

1000=

47. 0.15 0.16 ↑ ↑ 5 < 6 so 0.15 < 0.16

48. 0.12 0.15 ↑ ↑ 2 < 5 so 0.12 < 0.15

49. 0.57 0.54 ↑ ↑ 7 > 4 so 0.57 > 0.54 Thus −0.57 < −0.54.

50. 0.59 0.52 ↑ ↑ 9 > 2 so 0.59 > 0.52 Thus, −0.59 < −0.52.

51. 0.098 0.1 ↑ ↑ 0 < 1 so 0.098 < 0.1

52. 0.0756 0.2 ↑ ↑ 0 < 2 so 0.0756 < 0.2

53. 0.54900 0.549 ↑ ↑ 9 = 9 so 0.54900 = 0.549



228

54. 0.98400 0.984 ↑ ↑ 4 = 4 so 0.98400 = 0.984

55. 167.908 167.980 ↑ ↑ 0 < 8 so 167.908 < 167.980

56. 519.3405 519.3054 ↑ ↑ 4 > 0 so 519.3405 > 519.3054

57. 1.062 1.07 ↑ ↑ 6 < 7 so 1.062 < 1.07 Thus, −1.062 > −1.07.

58. 18.1 18.01 ↑ ↑ 1 > 0 so 18.1 > 18.01 Thus, −18.1 < −18.01.

59. −7.052 7.0052 ↑ ↑ − < + so −7.052 < 7.0052

60. 0.01 −0.1 ↑ ↑ + > − so 0.01 > −0.1

61. 0.023 0.024 ↑ ↑ 3 < 4 so 0.023 < 0.024 Thus, −0.023 > −0.024.

62. 0.562 0.652 ↑ ↑ 5 < 6 so 0.562 < 0.652 Thus, −0.562 > −0.652.

63. To round 0.57 to the nearest tenth, observe that the digit in the hundredths place is 7. Since this digit is at least 5, we add 1 to the digit in the tenths place. The number 0.57 rounded to the nearest tenth is 0.6.

64. To round 0.64 to the nearest tenth, observe that the digit in the hundredths place is 4. Since this digit is less than 5, we do not add 1 to the digit in the tenths place. The number 0.64 rounded to the nearest tenth is 0.6.

65. To round 98,207.23 to the nearest ten, observe that the digit in the ones place is 7. Since this digit is at least 5, we add 1 to the digit in the tens place. The number 98,207.23 rounded to the nearest ten is 98,210.

66. To round 68,934.543 to the nearest ten, observe that the digit in the ones place is 4. Since this digit is less than 5, we do not add 1 to the digit in the tens place. The number 68,934.543 rounded to the nearest ten is 68,930.



69. To round 0.5942 to the nearest thousandth, observe that the digit in the ten-thousandths place is 2. Since this digit is less than 5, we do not add 1 to the digit in the thousandths place. The number 0.5942 rounded to the nearest thousandth is 0.594.


71. To round π ≈ 3.14159265 to the nearest tenth, observe that the digit in the hundredths place is 4. Since this digit is less than 5, we do not add 1 to the digit in the tenths place. The number π ≈ 3.14159265 rounded to the nearest tenth is 3.1.



229

72. To round π ≈ 3.14159265 to the nearest one, observe that the digit in the tenths place is 1. Since this digit is less than 5, we do not add 1 to the digit in the ones place. The number π ≈ 3.14159265 rounded to the nearest ones is 3.

73. To round π ≈ 3.14159265 to the nearest thousandth, observe that the digit in the ten-thousandth place is 5. Since this digit is at least 5, we add 1 to the digit in the thousandths place. The number π ≈ 3.14159265 rounded to the nearest thousandth is 3.142.

74. To round π ≈ 3.14159265 to the nearest hundred-thousandth, observe that the digit in the millionths place is 2. Since this digit is less than 5, we do not add 1 to the digit in the hundred-thousandths place. The number π ≈ 3.14159265 rounded to the nearest hundred-thousandth is 3.14159.

75. To round 26.95 to the nearest one, observe that the digit in the tenths place is 9. Since this digit is at least 5, we add 1 to the digit in the ones place. The number 26.95 rounded to the nearest one is 27. The amount is $27.

76. To round 14,769.52 to the nearest one, observe that the digit in the tenths place is 5. Since this digit is at least 5, we add 1 to the digit in the ones place. The number 14,769.52 rounded to the nearest one is 14,770. The amount is $14,770.

77. To round 0.1992 to the nearest hundredth, observe that the digit in the thousandths place is 9. Since this digit is at least 5, we add 1 to the digit in the hundredths place. The number 0.1992 rounded to the nearest hundredth is 0.2. The amount is $0.20.

78. To round 0.7633 to the nearest hundredth, observe that the digit in the thousandths place is 3. Since this digit is less than 5, we do not add 1 to the digit in the hundredths place. The number 0.7633 rounded to the nearest hundredth is 0.76. The amount is $0.76.

79. To round 10.414 to the nearest tenth, observe that the digit in the hundredths place is 1. Since this digit is less than 5, we do not add 1 to the digit in the tenths place. The number 10.414 rounded to the nearest tenth is 10.4. The length is 10.4 centimeters.

80. To round 3.36 to the nearest tenth, observe that the digit in the hundredths place is 6. Since this digit is at least 5, we add 1 to the digit in the tenths place. The number 3.36 rounded to the nearest tenth is 3.4. The speed is 3.4 mph.

81. To round 1.7283 to the nearest hundredth, observe that the digit in the thousandths place is 8. Since this digit is at least 5, we add 1 to the digit in the hundredths place. The number 1.7283 rounded to the nearest hundredth is 1.73. The time is 1.73 hours.

82. To round 102.5794 to the nearest tenth, observe that the digit in the hundredths place is 7. Since this digit is at least 5, we add 1 to the digit in the tenths place. The number 102.5794 rounded to the nearest tenth is 102.6. There are 102.6 people per square mile.

83. To round 47.89 to the nearest one, observe that the digit in the tenths place is 8. Since this digit is at least 5, we add 1 to the digit in the ones place. The number 47.89 rounded to the nearest one is 48. The price is $48.

84. To round 19.95 to the nearest one, observe that the digit in the tenths place is 9. Since this digit is at least 5, we add 1 to the digit in the ones place. The number 19.95 rounded to the nearest one is 20. The price is $20.

85. To round 24.6229 to the nearest thousandth, observe that the digit in the ten-thousandths place is 9. Since this digit is at least 5, we add 1 to the digit in the thousandths place. The number 24.6229 rounded to the nearest thousandth is 24.623. The day length is 24.623 hours.

86. To round 224.695 to the nearest one, observe that the digit in the tenths place is 6. Since this digit is at least 5, we add 1 to the digit in the ones place. The number 224.695 rounded to the nearest one is 225. This is 225 days.

87. 345223145766

+

88. 8 9454 536

13,481+



230

89. 824735

−

90. 40023897

105−

91. To round 2849.1738 to the nearest hundred, observe that the digit in the tens place is 4. Since this digit is less than 5, we do not add 1 to the digit in the hundreds place. The number 2849.1738 rounded to the nearest hundred is 2800, which is choice b.

92. To round 146.059 to the nearest ten, observe that the digit in the ones place is 6. Since this digit is at least 5, we add 1 to the digit in the tens place. The number 146.059 rounded to the nearest ten is 150, which is choice d.

93. To round 2849.1738 to the nearest hundredth, observe that the digit in the thousandths place is 3. Since this digit is less than 5, we do not add 1 to the digit in the hundredths place. 2849.1738 rounded to the nearest hundredth is 2849.17, which is choice a.

94. To round 146.059 to the nearest tenth, observe that the digit in the hundredths place is 5. Since this digit is at least 5, we add 1 to the digit in the tenths place. The number 146.059 rounded to the nearest tenth is 146.1, which is choice b.

95. answers may vary


97. 127 7.12100

=

98. 26817 17.268

1000=

99. 26,849,5760.00026849576

100,000,000,000=

100. 0.00026849576 in words is twenty-six million, eight hundred forty-nine thousand, five hundred seventy-six hundred-billionths.




104. 0.26499 and 0.25786 rounded to the nearest hundredth are 0.26. 0.26559 rounds to 0.27 and 0.25186 rounds to 0.25.

105. 0.0612 and 0.0586 rounded to the nearest hundredth are 0.06. 0.066 rounds to 0.07. 0.0506 rounds to 0.05.

106. From smallest to largest, 0.10299, 0.1037, 0.1038, 0.9

107. From smallest to largest, 0.01, 0.0839, 0.09, 0.1

108. Round to the nearest hundred million, then add. 600500400400400400

2700+

The total amount of money is estimated as $2700 million.

109. 602.2 rounded to the nearest ten is 600. 33.8 rounded to the nearest ten is 30. 600 2030

=

An individual music video has a value of approximately $20.

Section 5.2

Practice Problems

1. a. 19.5205.371

24.891+

b. 40.08017.61257.692

+

c. 0.125422.800422.925

+

2. a. 34.5670129.4300

2.8903166.8873

+



231

b. 11.21046.013

362.526419.749

+

3. 19.00026.07245.072

+

4. 7.12 + (−9.92) Subtract the absolute values.

9.927.122.80

−

Attach the sign of the larger absolute value. 7.12 + (−9.92) = −2.8

5. a. 6.703.922.78

− Check: 2.78

3.926.70

+

b. 9.7204.0685.652

− Check: 5.652

4.0689.720

+

6. a. 73.0029.3143.69

− Check: 43.69

29.3173.00

+

b. 210.0068.22

141.78−

Check: 141.7868.22

210.00+

7. 25.9119.00

6.91−

8. −5.4 − 9.6 = −5.4 + (−9.6) Add the absolute values.

5.49.6

15.0+

Attach the common sign. −5.4 − 9.6 = −15

9. −1.05 − (−7.23) = −1.05 + 7.23 Subtract the absolute values.

7.231.056.18

−

Attach the sign of the larger absolute value. −1.05 − (−7.23) = 6.18

10. a. Exact Estimate 1 Estimate 2 58.10

326.97385.07

+ 60

300360

+ 60

330390

+

b. Exact Estimate 1 Estimate 2 16.080

0.92515.155

− 16

115

− 20

119

−

11. y − z = 11.6 − 10.8 = 0.8

12. 4.3 7.812.1 4.3 7.8

7.8 7.8 True

y − =−

=�

Yes, 12.1 is a solution.

13. 4.3 7.8 20.1 14.64.3 20.1 7.8 14.6

( 4.3 20.1) (7.8 14.6)24.4 22.4

y yy y

yy

− + − += − − + += − − + += − +

14. 563.5252.68

127.50743.70

+

The total cost is $743.70.

15. 72.670.81.8

−

The average height in the Netherlands is 1.8 inches greater than the average height in Czechoslovakia.

Calculator Explorations

1. 315.782 + 12.96 = 328.742

2. 29.68 + 85.902 = 115.582

3. 6.249 − 1.0076 = 5.2414

4. 5.238 − 0.682 = 4.556

5. 12.555224.987

5.2622.65865.392

+



232

6. 47.0060.17

313.259139.088499.523

+


1. The decimal point in a whole number is positioned after the last digit.

2. In 89.2 − 14.9 = 74.3, the number 74.3 is called the difference, 89.2 is the minuend, and 14.9 is the subtrahend.

3. To simplify an expression, we combine any like terms.

4. True or false: If we replace x with 11.2 and y with −8.6 in the expression x − y, we have 11.2 − 8.6. false

5. To add or subtract decimals, we line up the decimal points vertically.

Exercise Set 5.2

1. 5.62.17.7

+

2. 3.64.17.7

+

3. 8.202.15

10.35+

4. 5.173.708.87

+

5. 24.60002.39000.0678

27.0578+

6. 32.40001.58000.0934

34.0734+

7. −2.6 + (−5.97) Add the absolute values.

2.605.978.57

+

Attach the common sign. −2.6 + (−5.97) = −8.57

8. −18.2 + (−10.8) Add the absolute values.

18.210.829.0

+

Attach the common sign. −18.2 + (−10.8) = −29

9. 18.56 + (−8.23) Subtract the absolute values. 18.56

8.2310.33−

Attach the sign of the larger absolute value. 18.56 + (−8.23) = 10.33

10. 4.38 + (−6.05) Subtract the absolute values.

6.054.381.67

−

Attach the sign of the larger absolute value. 4.38 + (−6.05) = −1.67

11. Exact: 234.89230.67465.56

+

Estimate: 230230460

+

12. Exact: 734.89640.56

1375.45+

Estimate: 730640

1370+



233

13. Exact: 100.0096.0809.034

115.123+

Estimate: 10069

115+

14. Exact: 200.897.49

62.83271.21

+

Estimate: 2007

60267

+

15. 39.0003.0068.403

50.409+

16. 65.00005.09036.9003

76.9906+

17. 12.68.24.4

− Check: 4.4

8.212.6+

18. 8.93.15.8

− Check: 5.8

3.18.9

+

19. 18.02.7

15.3−

Check: 15.32.7

18.0+

20. 28.03.3

24.7−

Check: 24.73.3

28.0+

21. 654.9056.67

598.23−

Check: 598.2356.67

654.90+

22. 863.23039.453

823.777−

Check: 823.77739.453

863.230+

23. Exact: 5.9 − 4.07 = 1.83 Estimate: 6 − 4 = 2 Check: 1.83 + 4.07 = 5.90

24. Exact: 6.4 − 3.04 = 3.36 Estimate: 6 − 3 = 3 Check: 3.36 + 3.04 = 6.40

25. Exact: 1000.0123.4876.6

− Check: 876.6

123.41000.0+

Estimate: 1000

100900

−

26. Exact: 2000.00327.47

1672.53−

Check: 1672.53327.47

2000.00+

Estimate: 2000300

1700−

27. 200.05.6

194.4−

28. 80008.9

791.1−


1.125.206.32

+

Attach the common sign. −1.12 − 5.2 = −6.32


8.635.60

14.23+




234

31. 5.21 − 11.36 = 5.21 + (−11.36) Subtract the absolute values.

11.365.216.15

−

Attach the sign of the larger absolute value. 5.21 − 11.36 = −6.15


17.848.539.31

−



5.72.63.1

−

Attach the sign of the larger absolute value. −2.6 − (−5.7) = 3.1


10.49.41.0

−

Attach the sign of the larger absolute value. −9.4 − (−10.4) = 1

35. 3.00000.00122.9988

−

36. 7.0000.0976.903

−

37. 23.06.7

16.3−

38. 45.09.2

35.8−

39. 0.92.23.1

+

40. 0.73.44.1

+

41. −6.06 + 0.44 Subtract the absolute values.

6.060.445.62

−

Attach the sign of the larger absolute value. −6.06 + 0.44 = −5.62


5.050.884.17

−


43. 500.21136.85363.36

−

44. 600.47254.68345.79

−

45. 50.2 − 600 = 50.2 + (−600) Subtract the absolute values.

600.050.2

549.8−

Attach the sign of the larger absolute value. 50.2 − 600 = −549.8

46. 40.3 − 700 = 40.3 + (−700) Subtract the absolute values.

700.040.3

659.7−

Attach the sign of the larger absolute value. 40.3 − 700 = −659.7

47. 923.561.9

861.6−

48. 845.945.8

800.1−



235

49. 100.0096.0809.034

115.123+

50. 200.897.49

62.83271.21

+


0.0910.0030.088

−

Attach the sign of the larger absolute value. −0.003 + 0.091 = 0.088


0.0850.0040.081

−

Attach the sign of the larger absolute value. −0.004 + 0.085 = 0.081


102.4078.04

180.44+



36.2010.0246.22

+



2.91.81.1

−

Attach the sign of the larger absolute value. −2.9 − (−1.8) = −1.1


6.53.33.2

−

Attach the sign of the larger absolute value. −6.5 − (−3.3) = −3.2

57. x + z = 3.6 + 0.21 = 3.81

58. y + x = 5 + 3.6 = 8.6

59. x − z = 3.6 − 0.21 = 3.39

60. y − z = 5 − 0.21 = 4.79

61. 5 3.6 0.215.00 3.60 0.211.40 0.211.61

y x z− + = − += − += +=

62. x + y + z = 3.6 + 5 + 0.21 = 8.6 + 0.21 = 8.81

63. 2.7 9.37 2.7 9.3

9.7 9.3 False

x + =+

=�

No, 7 is not a solution.

64. 5.9 8.63.7 5.9 8.6

9.6 8.6 False

x + =+

=�

No, 3.7 is not a solution.

65. 27.4 1627.4 ( 11.4) 16

16 16 True

y+ =+ −

=�

Yes, −11.4 is a solution.

66. 45.9 2345.9 ( 22.9) 23

23 23 True

z+ =+ −

=�


67. 2.3 5.32.3 1 5.3 1

3.3 4.3 False

x x+ = −+ −

=�


68. 1.9 0.11.9 0.9 0.9 0.1

1 1 True

x x− = +− +

=�




236

69. 30.7 17.6 23.8 10.730.7 23.8 17.6 10.7(30.7 23.8) (17.6 10.7)6.9 6.9

x xx x

xx

+ − −= − + −= − + −= +

70. 14 11.9 9.6 15.214.2 9.6 11.9 15.2(14.2 9.6) (11.9 15.2)4.6 3.3

z zz z

zz

+ − −= − + −= − + −= −

71. 8.61 4.23 2.36 0.764.23 0.76 8.61 2.36(4.23 0.76) ( 8.61 2.36)3.47 10.97

y yy y

yy

− + − −= − − −= − + − −= −

72. 8.96 2.31 4.08 9.688.96 4.08 2.31 9.68

( 8.96 4.08) ( 2.31 9.68)13.04 7.37

x xx x

xx

− − − += − − − += − − + − += − +

73. Subtract the opening price from the closing price.

22.0721.900.17

−

The price of each share increased by $0.17.

74. Subtract the cost of the frames from the cost of the glasses.

347.8997.23

250.66−

The lenses cost $250.66.

75. Perimeter 7.14 7.14 7.14 7.1428.56 meters

= + + +=

76. Perimeter =4.2 + 5.78 + 7.8 = 17.78 inches

77. Perimeter = 3.6 + 2.0 + 3.6 + 2.0 = 11.2 inches

78. Perimeter = 4.1 + 2.4 + 4.1 + 2.4 = 13 inches

79. 40.0032.487.52

−

The change was $7.52.

80. 20.0018.26

1.74−

The change was $1.74.

81. The phrase “How much faster” indicates that we should subtract the average wind speed from the record speed.

321.035.2

285.8−

The highest wind speed is 285.8 miles per hour faster than the average wind speed.

82. The phrase “how much more” indicates that we should subtract the average rainfall in Omaha from that of New Orleans.

61.8830.2231.66

−

Therefore, on average New Orleans receives 31.66 inches more rain than Omaha.

83. 10.47.03.4

−

The decrease in revenue is predicted to be $3.4 billion.

84. 24.615.3

9.3−

The increase is predicted to be $9.3 billion.

85. To find the total, we add. 600.78460.99436.72

1498.49+

The total ticket sales were $1498.49 million.

86. To find the increase, subtract. 29.4512.5316.92

−

The average late fee increased by $16.92.

87. To find the amount of snow in Blue Canyon, add 111.6 to the amount in Marquette.

129.2111.6240.8

+

Blue Canyon receives on average 240.8 inches each year.



237

88. To find the amount of rainfall in Yuma, add 0.02 to the amount in Aswan.

0.022.632.65

+

Yuma receives an average of 2.65 inches of rainfall each year.

89. Add the lengths of the sides to get the perimeter. 12.4029.3425.7067.44

+

67.44 feet of border material is needed.

90. Add the lengths of the sides to get the perimeter. 15.710.615.710.652.6

+

Therefore, 52.6 feet of railing was purchased.

91. 160.927142.734

18.193−

The difference is 18.193 miles per hour.

92. 154.308148.124

6.184−

The difference is 6.184 miles per hour.

93. The tallest bar indicates the greatest chocolate consumption per person, so Switzerland has the greatest chocolate consumption per person.

94. The shortest bar indicates the least consumption per person, so Belgium has the least chocolate consumption per person.

95. 22.013.9

8.1−

The difference in consumption is 8.1 pounds per year.

96. 15.814.5

1.3−

The difference in consumption is 1.3 pounds per year.

97. Country

Pounds of Chocolate per Person

Switzerland 22.0

Norway 16.0

Germany 15.8

United Kingdom 14.5

Belgium 13.9

98. 23 ⋅ 2 = 46

99. 46 ⋅ 3 = 138

100. 22 2 2 2 2 4

3 3 3 3 3 9⋅⎛ ⎞ = ⋅ = =⎜ ⎟ ⋅⎝ ⎠

101. 31 1 1 1 1 1 1 1

5 5 5 5 5 5 5 125⋅ ⋅⎛ ⎞ = ⋅ ⋅ = =⎜ ⎟ ⋅ ⋅⎝ ⎠

102. It is incorrect. Align the decimals. 9.2008.6304.005

21.835+

103. 10.68 − (2.3 + 2.3) = 10.68 − 4.60 = 6.08 The unknown length is 6.08 inches.

104. 17.67 − (5.26 + 7.82) = 17.67 − 13.08 = 4.59 The unknown length is 4.59 meters.

105. 3 nickels, 3 dimes, and 3 quarters: 0.05 + 0.05 + 0.05 + 0.10 + 0.10 + 0.10 + 0.25 + 0.25 + 0.25 = 1.2 The value of the coins shown is $1.20.

106. 2 quarters, 3 dimes, 4 nickels, and 2 pennies: 0.25 + 0.25 + 0.10 + 0.10 + 0.10 + 0.05 + 0.05 + 0.05 + 0.05 + 0.01 + 0.01 = 1.02 The value of the coins shown is $1.02.

107. 1 nickel, 1 dime, and 2 pennies: 0.05 + 0.10 + 0.01 + 0.01 = 0.17 3 nickels and 2 pennies: 0.05 + 0.05 + 0.05 + 0.01 + 0.01 = 0.17 1 dime and 7 pennies: 0.10 + 0.01 + 0.01 + 0.01 + 0.01 + 0.01 + 0.01 + 0.01 = 0.17



238

108. 5 nickels: 0.05 + 0.05 + 0.05 + 0.05 + 0.05 = 0.25 1 dime and 3 nickels: 0.10 + 0.05 + 0.05 + 0.05 = 0.25 2 dimes and 1 nickel: 0.10 + 0.10 + 0.05 = 0.25 1 quarter: 0.25



111. 256,436.012256, 435.235

0.777−

The difference in measurements is 0.777 mile.

112. −8.689 + 4.286x − 14.295 − 12.966x + 30.861x = 4.286x − 12.966x + 30.861x − 8.689 − 14.295 = (4.286 − 12.966 + 30.861)x + (−8.689 − 14.295) = 22.181x − 22.984

113. 14.271 − 8.968x + 1.333 − 201.815x + 101.239x = −8.968x − 201.815x + 101.239x + 14.271 + 1.333 = (−8.968 − 201.815 + 101.239)x + (14.271 + 1.333) = −109.544x + 15.604

114. no; answers may vary

Section 5.3

Practice Problems

1. 34.8 1 decimal place0.62 2 decimal places696

20 88021.576 1 2 3 decimal places

×

+ =

2. 0.0641 4 decimal places27 0 decimal places

44871 28201.7307 4 0 4 decimal places

×

+ =

3. (7.3)(−0.9) = −6.57 (Be sure to include the negative sign.)

4. Exact: 30.262.89

2 723424 208060 520087.4514

× Estimate: 30

390

×

5. 46.8 × 10 = 468

6. 203.004 × 100 = 20,300.4

7. (−2.33)(1000) = −2330

8. 6.94 × 0.1 = 0.694

9. 3.9 × 0.01 = 0.039

10. (−7682)(−0.001) = 7.682

11. 76.2 million 76.2 1 million76.2 1,000,00076, 200,000

= ×= ×=

12. 7y = 7(−0.028) = −0.196

13. 6 336( 5.5) 33

33 33 True

x− =− −

=�


14. C = 2πr = 2π ⋅ 11 = 22π ≈ 22(3.14) = 69.08 The circumference is 22π meters ≈ 69.08 meters.

15. 60.55.6

36 30302 50338.80

×

She needs 338.8 ounces of fertilizer.


1. When multiplying decimals, the number of decimal places in the product is equal to the sum of the number of decimal place in the factors.

2. In 8.6 × 5 = 43, the number 43 is called the product while 8.6 and 5 are each called a factor.

3. When multiplying a decimal number by powers of 10 such as 10, 100, 1000, and so on, we move the decimal point in the number to the right the same number of places as there are zeros in the power of 10.



239

4. When multiplying a decimal number by powers of 10 such as 0.1, 0.01, and so on, we move the decimal point in the number to the left the same number of places as there are decimal places in the power of 10.

5. The distance around a circle is called its circumference.

Exercise Set 5.3


1.36 2 0 2 decimal places×

+ =



+ =

3. 1.2 1 decimal place0.5 1 decimal place


+ =

4. 6.8 1 decimal place0.3 1 decimal place


+ =

5. The product (−2.3)(7.65) is negative. 7.65 2 decimal places

2.3 1 decimal place2 295

15 30017.595 2 1 3 decimal places and

×

− + =

include the negative sign

6. The product (4.7)(−9.02) is negative. 9.02 2 decimal places4.7 1 decimal place

6 31436 08042.394 2 1 3 decimal places and

×

− + =

include the negative sign.

7. The product (−5.73)(−9.6) is positive. 5.73 2 decimal places9.6 1 decimal place

3 43851 57055.008 2 1 3 decimal places

×

+ =

8. The product (−7.84)(−3.5) is positive. 7.84 3 decimal places

3.5 1 decimal place3 920

23 52027.440 2 1 3 decimal places

×

+ =

9. Exact: 6.84.2

1 3627 2028.56

× Estimate: 7

428×

10. Exact: 8.32.7

5 8116 6022.41

× Estimate: 8

324×

11. 0.347 3 decimal places0.3 1 decimal place


+ =



+ =

13. Exact: 1.00478.2

200948 037608.23854

× Estimate: 1

88

×

14. Exact: 2.00055.5

1 0002510 0025011.00275

× Estimate: 2

612

×

15. 490.2 1 decimal place0.023 3 decimal places

1 47069 8040

11.2746 1 3 4 decimal places

×

+ =



240


9 02709.6288 1 3 4 decimal places

×

+ =

17. 6.5 × 10 = 65

18. 7.2 × 100 = 720

19. 8.3 × 0.1 = 0.83

20. 23.4 × 0.1 = 2.34

21. (−7.093)(1000) = −7093

22. (−1.123)(1000) = −1123

23. 7.093 × 100 = 709.3

24. 0.5 × 100 = 50

25. (−9.83)(−0.01) = 0.0983

26. (−4.72)(−0.01) = 0.0472

27. 25.23 × 0.001 = 0.02523

28. 36.41 × 0.001 = 0.03641

29. 0.1230.4

0.0492×

30. 0.2160.3

0.0648×

31. (147.9)(100) = 14,790

32. (345.2)(100) = 34,520

33. 8.60.15430860

1.290

×

or 1.29

34. 0.425.7294

2 1002.394

×

35. (937.62)(−0.01) = −9.3762

36. (−0.001)(562.01) = −0.56201

37. 562.3 × 0.001 = 0.5623

38. 993.5 × 0.001 = 0.9935

39. 6.325.7

4 42431 60036.024

×

40. 9.213.8

7 36827 63034.998

×

41. 1.5 billion 1.5 1 billion1.5 1,000,000,0001,500,000,000

= ×= ×=

The cost at launch was $1,500,000,000.

42. 40.4 million 40.4 1 million40.4 1,000,00040,400,000

= ×= ×=

About 40,400,000 American households own at least one dog.

43. 49.8 million 49.8 1 million49.8 1,000,00049,800,000

= ×= ×=

The roller coaster has given more than 49,800,000 rides.

44. 166.2 thousand 166.2 1 thousand166.2 1000166, 200

= ×= ×=

There are 166,200 full service restaurants in the United States.

45. xy = 3(−0.2) = −0.6

46. yz = (−0.2)(5.7) = −1.14

47. 3(5.7) ( 0.2)17.1 ( 0.2)17.1 0.217.3

xz y− = − −= − −= +=



241

48. −5y + z = −5(−0.2) + 5.7 = 1.0 + 5.7 = 6.7

49. 0.6 4.920.6(14.2) 4.92

8.52 4.92 False

x =

=�

No, 14.2 is not a solution.

50. 100 14.14100(1414) 14.14

141, 400 14.14 False

z =

=�


51. 3.5 143.5( 4) 14

14 14 True

y = −− −− = −

�

Yes, −4 is a solution.

52. 0.7 2.520.7( 3.6) 2.52

2.52 2.52 True

x = −− −− = −

�


53. C = πd is π(10 cm) = 10π cm C ≈ 10(3.14) cm = 31.4 cm

54. C = πd is π(22 inches) = 22π inches C ≈ 22(3.14) inches = 69.08 inches

55. C = 2πr is 2π ⋅ 9.1 yards = 18.2 yards C ≈ 18.2(3.14) yards = 57.148 yards

56. C = 2πr is 2π ⋅ 5.9 kilometers = 11.8π kilometers 11.8(11.8)(3.14) kilometers37.052 kilometers

C ≈ π==

57. Multiply the number of ounces by the number of grams of saturated fat in 1 ounce.

6.24

24.8×

There are 24.8 grams of saturated fat in a 4-ounce serving of cream cheese.

58. Multiply the number of servings by the number of grams of saturated fat in 3.5 ounces. 3 × 0.1 = 0.3 There is 0.3 gram of saturated fat in 3 servings.

59. Area = length ⋅ width 3.62.0

7.20×

The area is 7.2 square inches.

60. Area = length ⋅ width 4.12.4

1 648 209.84

×

The area is 9.84 square inches.

61. Circumference = π ⋅ diameter C = π ⋅ 250 = 250π

2503.14

10 0025 00

750 00785.00

×

The circumference is 250π feet, which is approximately 785 feet.

62. Circumference = 2 ⋅ π ⋅ radius C = 2 ⋅ π ⋅ 3950 = 7900π

79003.14

316 00790 00

23700 0024806.00

×

The circumference is 7900π miles, which is approximately 24,806 miles.

63. C = π ⋅ d C = π ⋅ 135 = 135π

1353.145 40

13 50405 00423.90

×

He travels 135π meters or approximately 423.9 meters.



242

64. C = π ⋅ d C = π ⋅ 80 = 80π

3.1480

251.20×

The circumference is 80π meters or approximately 251.2 meters.

65. Multiply her height in meters by the number of inches in 1 meter.

39.371.65

1 968523 622039 370064.9605

×

She is approximately 64.9605 inches tall.

66. Multiply the doorway height in meters by the number of inches in 1 meter.

39.372.15

1 96853 9370

78 740084.6455

×

The doorway is approximately 84.6455 inches.

67. 17.8840

715.20×

His pay for last week was $715.20.

68. 19.5220

390.40×

Her pay for last week was $390.40.

69. a. Circumference = 2 ⋅ π ⋅ radius Smaller circle: C = 2 ⋅ π ⋅ 10 = 20π C ≈ 20(3.14) = 62.8 The circumference of the smaller circle is approximately 62.8 meters. Larger circle: C = 2 ⋅ π ⋅ 20 = 40π C ≈ 40(3.14) = 125.6 The circumference of the larger circle is approximately 125.6 meters.

b. Yes, the circumference gets doubled when the radius is doubled.

70. a. Circumference = π ⋅ diameter Smaller circle: C = π ⋅ 16 = 16π C ≈ 16(3.14) = 50.24 The circumference of the smaller circle is approximately 50.24 inches. Larger circle: C = π ⋅ 32 = 32π C ≈ 32(3.14) = 100.48 The circumference of the larger circle is approximately 100.48 inches.

b. Yes, the circumference gets doubled when the diameter is doubled.

71. 3.40 × 100 = 340 The farmer received $340.

72. 5.5 × 10,000 = 55,000 The farmer received $55,000.

73. 115.26675

576 308 068 20

69 156 0077,800.50

×

675 U.S. Dollars is equivalent to 77,800.5 Japanese yen.

74. 8.0035500

4001.7500×

500 U.S. Dollars is equivalent to 4001.75 Chinese yuan.

75. 0.7951900

715.5900×

900 U.S. Dollars will buy 715.59 European Union euros.

76. 1.355985

6 7795108 4720115.2515

×

He paid 115.25 Australian dollars.



243

77. 8

365 29202920

0−

78. 486

6 2916245148

3636

0

−

−

−

79. 24 8 24 21 8 3 7 3 3 3 97 21 7 8 7 8 1

⋅ ⋅ ⋅ ⋅− ÷ = − ⋅ = − = − = −

⋅

80. 162 9 162 7525 75 25 9

9 18 25 325 9

18 31

54

÷− = ⋅−

⋅ ⋅ ⋅= −

⋅⋅

= −

= −

81. 3.600.043.64

+

82. 3.60.04

0.144

−×−

83. 3.600.043.56

−

84. 100.048.651.4

−

85. 0.2210.5

0.1105

−×−

86. 7.200.14

98.60105.94

+

87. 20.61.86

1 23616 48020 60038.316

×

38.316 × 100,000 = 3,831,600 The radio wave travels 3,831,600 miles in 20.6 seconds.

88. 8.3 minutes = 8.3 × 60 seconds = 498 seconds 498

1.8629 88

398 40498 00926.28

×

926.28 × 100,000 = 92,628,000 The radio wave travels 92,628,000 miles.




Section 5.4

Practice Problems

1. 46.3

8 370.432

50482 42 4

0

−

−

−

Check: 46.38

370.4×

2. 0.71

48 34.0833 6

48480

−

−

Check: 0.7148

5 6828 4034.08

×



244

3. a. 1.135

14 15.89014

1 81 4

4942

70700

−

−

−

−

Check: 1.13514

4 54011 35015.890

×

Thus, −15.89 ÷ 14 = −1.135.

b. 0.027

104 2.8082 08

728728

0

−

−

Check: 0.027104108

2 7002.808

×

Thus, −2.808 ÷ (−104) = 0.027

4. 5.6 166.88 becomes 29.8

56 1668.811254850444 844 8

0

−

−

−

5. 0.16 1.976 becomes 12.35

16 197.6016

37325648

80800

−

−

−

−

6. 0.57 23.4 becomes 41.052 41.05

57 2340.000228

60573 002 85

15011436

≈

−

−

−

−

7. 91.5 713.7 becomes 7.8

915 7137.06405732 0732 0

0

−

−

Estimate: 7

100 700

8. 362.1 0.3621100

=

9. 0.49 0.04910

− = −

10. x ÷ y = 0.035 ÷ 0.02

0.02 0.035 becomes 1.75

2 3.5021 51 4

1010

0

−

−

−

11. 3.910039 3.9

1000.39 3.9 False

x=

=

�




245

12. 11.84

1250 14800.001250

230012501050010000

50005000

0

−

−

−

−

He needs 11.84 bags or 12 whole bags.

Calculator Explorations

1. 102.62 × 41.8 ≈ 100 × 40 = 4000 Since 4000 is not close to 428.9516, it is not reasonable.

2. 174.835 ÷ 47.9 ≈ 200 ÷ 50 = 4 Since 4 is close to 3.65, it is reasonable.

3. 1025.68 − 125.42 ≈ 1000 − 100 = 900 Since 900 is close to 900.26, it is reasonable.

4. 562.781 + 2.96 ≈ 563 + 3 = 566 Since 566 is not close to 858.781, it is not reasonable.


1. In 6.5 ÷ 5 = 1.3, the number 1.3 is called the quotient, 5 is the divisor, and 6.5 is the dividend.

2. To check a division exercise, we can perform the following multiplication: quotient ⋅ divisor = dividend.

3. To divide a decimal number by a power of 10 such as 10, 100, 1000, or so on, we move the decimal point in the number to the left the same number of places as there are zeros in the power of 10.

4. True or false: If we replace x with −12.6 and y with 0.3 in the expression y ÷ x, we have 0.3 ÷ (−12.6) true

Exercise Set 5.4

1. 4.6

6 27.6243 63 6

0

−

−

2. 5.9

4 23.6203 63 6

0

−

−

3. 0.094

5 0.47045

2020

0

−

−

4. 0.085

6 0.51048

30300

−

−

5. 0.06 18 becomes 300

6 180018000

−

6. 0.04 20 becomes 500

4 200020000

−

7. 0.82 4.756 becomes 5.8

82 475.641065 665 6

0

−

−



246

8. 0.92 3.312 becomes 3.6

92 331.227655 255 2

0

−

−

9. Exact: 5.5 36.3 becomes 6.6

55 363.033033 033 0

0

−

−

Estimate: 6

6 36

10. Exact: 2.2 21.78 becomes 9.9

22 217.819819 819 8

0

−

−

Estimate: 11

2 22

11. 0.413

18 7.4347 2

2318

5454

0

−

−

−

12. 0.519

16 8.3048 0

3016144144

0

−

−

−

13. A positive number divided by a negative number is a negative number.

0.06 36 becomes 600

6 3600360

−

36 ÷ (−0.06) = −600

14. A positive number divided by a negative number is a negative number.

0.04 36 becomes 900

4 360036000

−

36 ÷ (−0.04) = −900

15. A negative number divided by a negative number is a positive number.

0.6 4.2 becomes 7

6 42420

−

(−4.2) ÷ (−0.6) = 7


0.9 3.6 becomes 4

9 36360

−

(−3.6) ÷ (−0.9) = 4

17. 0.27 1.296 becomes 4.8

27 129.6108

21 621 6

0

−

−

18. 0.34 2.176 becomes 6.4

34 217.620413 613 6

0

−

−

19. 0.02 42 becomes 2100

2 42004022000

−

−



247

20. 0.03 24 becomes 800

3 240024000

−

21. 0.82 4.756 becomes 5.8

82 475.641065 665 6

0

−

−

22. 0.92 3.312 becomes 3.6

92 331.227655 255 2

0

−

−


6.6 36.3 becomes 5.5

66 363.033033 033 0

0

−

−

−36.3 ÷ −6.6 = 5.5


9.9 21.78 becomes 2.2

99 217.819819 819 8

0

−

−

−21.78 ÷ −9.9 = 2.2

25. Exact: 7.2 70.56 becomes 9.8

72 705.664857 657 6

0

−

−

Estimate: 10

7 70

26. Exact: 6.3 54.18 becomes 8.6

63 541.850437 837 8

0

−

−

Estimate: 9

6 54

27. 5.4 51.84 becomes 9.6

54 518.448632 432 4

0

−

−

28. 7.7 33.88 becomes 4.4

77 338.830830 830 8

0

−

−

29. 0.027 1.215 becomes 45

27 1215108135135

0

−

−

1.215 450.027

=

30. 0.051 3.213 becomes 63

51 3213306153153

0

−

−

3.213 630.051

=



248

31.

0.25 13.648 becomes 54.592

25 1364.800125114100

14 812 5

2 302 25

50500

−

−

−

−

−

32.

0.75 49.866 becomes 66.488

75 4986.600450

48645036 630 06 606 00

600600

0

−

−

−

−

−

33. 3.78 0.02079 becomes 0.0055

378 2.07901 890

18901890

0

−

−

34. 2.96 0.01332 becomes 0.0045

296 1.33201184

14801480

0

−

−

35.

0.023 0.549

becomes 23.869 23.87

23 549.00046

896920 018 41 601 38

220207

13

≈

−

−

−

−

−

36. 0.98 0.0453 becomes 0.0462 0.046

98 4.53003 92

610588

22019624

≈

−

−

−

37. 0.6 68.39 becomes 113.98 114.0

6 683.90608623185 95 4

50482

≈

−

−

−

−

−

38. 3.5 98.83 becomes 28.23 28.2

35 988.3070288280

837 01 301 05

25

≈

−

−

−

−

39. 83.397 0.83397

100=



249

40. 64.423 0.64423

100=

41. 26.87 2.687

10=

42. 13.49 1.349

10=

43. 12.9 ÷ (−1000) = −0.0129

44. 13.49 ÷ (−10,000) = −0.001349

45. 1.26

7 88.2718144 24 2

0

−

−

−

46. 14.5

9 130.5940364 54 5

0

−

−

−

47. 13.1 1.3110

=

48. 17.7 1.7710

=

49. 456.25 0.04562510,000

=

50. 986.11 0.09861110,000

=

51. 0.413

3 1.2391 2

0330990

−

−

−

52. 0.045

12 0.54048

6060

0

−

−

53. 0.6 4.2 becomes 7

6 42420

−

4.2 ÷ (−0.6) = −7

54. 0.9 3.6 becomes 4

9 36360

−

3.6 ÷ (−0.9) = −4

55. 0.27 1.296 becomes 4.8

27 129.6108

21 621 6

0

−

−

−1.296 ÷ 0.27 = −4.8

56. 0.34 2.176 becomes 6.4

34 217.620413 613 6

0

−

−

−2.176 ÷ 0.34 = −6.4



250

57. 0.02 42 becomes 2100

2 420040220

−

−

42 ÷ 0.02 = 2100

58. 0.03 24 becomes 800

3 240024000

−

24 ÷ 0.03 = 800

59. 0.6 18 becomes 30

6 18018

00−

−18 ÷ (−0.6) = 30

60. 0.4 20 becomes 50

4 20020

00−

20 ÷ 0.4 = 50

61. 0.0015 87 becomes 58,000

15 870,00075120120

0000

−

−

87 ÷ (−0.0015) = −58,000

62. 0.0007 35 becomes 50,000

7 350,0003500 000

−

35 ÷ (−0.0007) = −50,000

63. 1.6 1.104 becomes 0.69

16 11.04961 441 44

0

−

−

−1.104 ÷ 1.6 = −0.69

64. 0.98 2.156 becomes 2.2

98 215.619619 619 6

0

−

−

−2.156 ÷ 0.98 = −2.2

65. 2.42.4 ( 100) 0.024100−

− ÷ − = =−

66. 86.7986.79 ( 1000) 0.086791000

−− ÷ − = =

−

67. 0.071 4.615 becomes 65

71 4615426355355

0

−

−

4.615 650.071

=

68. 0.035 23.8 becomes 680

35 23800210280280

00

−

−

23.8 6800.035

=

69. z ÷ y = 4.52 ÷ (−0.8)

0.8 4.52 becomes 5.65

8 45.20405 24 8

40400

−

−

−

z ÷ y = 4.52 ÷ (−0.8) = −5.65



251

70. z ÷ x = 4.52 ÷ 5.65

5.65 4.52 becomes 0.8

565 452.0452 0

0−

z ÷ x = 4.52 ÷ 5.65 = 0.8

71. x ÷ y = 5.65 ÷ (−0.8)

0.8 5.65 becomes 7.0625

8 56.5000560 5

050482016

40400

−

−

−

−

−

x ÷ y = 5.65 ÷(−0.8) = −7.0625

72. y ÷ 2 = −0.8 ÷ 2 0.4

2 0.880−

y ÷ 2 = −0.8 ÷ 2 = −0.4

73. 3.044

12.16 3.0443.04 3.04 True

x=

=

�


74. 0.898

7.12 0.898

0.89 0.89 True

y=

=

�


75. 0.81008 0.8

1000.08 0.8 False

z=

=

�


76. 0.231023 0.23102.3 0.23 False

x=

=

�


77. 10.5 11

52 546.052

260

26 026 0

≈

−

−

−

Since he must buy whole quarts, 11 quarts are needed.

78. 1.5 740 becomes 493.33 493.3

15 7400.0060140135

5045

5045

50455

≈

−

−

−

−

−

Approximately 493.3 pages can be stored on one computer disk.

79. 39.37 200 becomes 5.08 5.1

3937 20000.0019685

315 00

3150031496

4

≈

−

−

−

There are approximately 5.1 meters in 200 inches.



252

80. 2.54 50 becomes 19.68 19.7

254 5000.00254246022861740152 421 6020 32

1 28

≈

−

−

−

−

There are approximately 19.7 inches in 50 centimeters.

81. Divide the number of crayons by 64. 11.40 11.4

64 730.0064

906426 025 6

40

≈

−

−

−

740 crayons is approximately 11.4 boxes.

82. Divide the price per hundred pounds by 100. 41.96 0.4196 0.42100

= ≈

The average price per pound was $0.42.

83. 6 × 4 = 24 There are 24 teaspoons in 4 fluid ounces.

84. Each dose is 0.5 teaspoon.

0.5 24 becomes 48

5 24020

40400

−

−

There are 48 doses in the bottle.

85. From Exercise 83, we know that there are 24 teaspoons in 4 fluid ounces. Thus, there are 48 half teaspoons (0.5 tsp) or doses in 4 fluid ounces. To see how long the medicine will last, if a dose is taken every 4 hours, there are 24 ÷ 4 = 6 doses taken per day. 48 (doses) ÷ 6 (per day) = 8 days. The medicine will last 8 days.

86. From Exercise 83, we know there are 24 teaspoons in 4 fluid ounces. Thus, there are 48 half teaspoons (0.5 tsp) or doses in 4 fluid ounces. To see how long the medicine will last, if a dose is taken every 6 hours, there are 24 ÷ 6 = 4 doses taken per day. 48 (doses) ÷ 4 (per day) = 12 days. The medicine will last 12 days.

87. There are 52 weeks in 1 year. 248.07

52 12,900.0010 4

2 502 08

420416

4 00

400364

36

−

−

−

−

−

Americans aged 18−22 drive, on average, 248.1 miles per week.

88. 19.35 423.8 becomes 21.90 21.9

1935 42380.003870

368019351745017415

350

≈

−

−

−

Javier’s car averages about 21.9 miles per gallon.

89. 5240

2080×

There are 2080 hours in 52 40-hour weeks.



253

5109.615 5109.622080 10,628,000.000

10 400228 0208 020 00

020 00018 7201 280 01 248 0

32 0020 8011 20010 400

800

≈

−

−

−

−

−

−

−

His hourly wage would have been $5109.62.

90. 287.5

24 6900.0482101921801681 201 20

0

−

−

−

−

There were 287.5 thousand books sold each hour.

91. 3 7 3 7 215 10 5 10 50

⋅⋅ = =

⋅

92. 3 7 3 10 3 10 3 5 2 65 10 5 7 5 7 5 7 7

⋅ ⋅ ⋅÷ = ⋅ = = =

⋅ ⋅

93. 3 7 3 2 7 6 7 15 10 5 2 10 10 10 10− = ⋅ − = − = −

94. 3 1 3 7 1 2 21 2 234 14 4 7 14 2 28 28 28

− − = − ⋅ − ⋅ = − − = −

95. 0.3 1.278 becomes 4.26

3 12.78120 7

618180

−

−

−



+ =

97. 1.2780.3001.578

+

98. 1.2780.3000.978

−

99. 8.6 1 decimal place3.1 1 decimal place86

25 8026.66 1 1 2 decimal places

×

+ =

(−8.6)(3.1) = −26.66

100. 7.200.05

49.1056.35

+

101. 1000.0095.71

904.29−

102. 87.2 0.00872

10,000= −

−

103. 8.62 × 41.7 is approximately 9 × 40 = 360, which is choice c.

104. 1.437 + 20.69 is approximately 1 + 21 = 22, which is choice b.

105. 78.6 ÷ 97 is approximately 78.6 ÷ 100 = 0.786, which is choice b.

106. 302.729 − 28.697 is approximately 300 − 30 = 270, which is choice a.



254

107. 86 78 91 87 342 85.5

4 4+ + +

= =

108. 56 75 80 211 70.3

3 3+ +

= ≈

109. Area = (length)(width)

4.5 38.7 becomes 8.6

45 387.036027 027 0

0

−

−

The length is 8.6 feet.

110. 45.2

4 180.816

2020

0 880

−

−

−

The length of a side is 45.2 centimeters.



113. 1.15 75 becomes 65.21 65.2

115 7500.00690

600575

250230

200115

85

≈

−

−

−

−

1.15 95 becomes 82.60 82.6

115 9500.00920

300230

700690

1000

100

≈

−

−

−

−

The range of wind speeds is 65.2−82.6 knots.

114. 1.15 131 becomes 113.91 113.9

115 13100.00115

160115

45034510501035

15011535

≈

−

−

−

−

−

1.15 155 becomes

134.78 134.8115 15500.00

115400345

550460900805

950920

30

≈

−

−

−

−

−

The range of wind speeds is 113.9 − 134.8 knots.

115. First find the length for one round of wire. Then multiply by 4.

24.28015.67524.28015.67579.910

+

79.914

319.64×

He will need 319.64 meters of wire.



255

116. 185.35 2523.86 becomes 13.6

18535 252386.018535

670365560511431 011121 0

310 0

−

−

−

No; it will take her more than 13 months to pay it off at the minimum rate.

The Bigger Picture

1. 3.6008.092

10.48022.172

+

2. 7.0003.0493.951

−

3. 91.332 × 100 = 9133.2

4. 68 6.810

− = −



×

+ =

6. 8.66

9 77.94725 95 4

54540

−

−

−

7. 0.35 0.01785 becomes 0.051

35 1.7851 75

35350

−

−

8. 22.3 (0.4) 2.30 0.16 2.14− = − =

9. 8 2 8 2 3 8 6 8 6 2

15 5 15 5 3 15 15 15 15−

− = − ⋅ = − = =

10. 8 2 8 2 16

15 5 15 5 75⋅

− ⋅ = − = −⋅

Integrated Review

1. 1.600.972.57

+

2. 3.200.854.05

+

3. 9.80.98.9

−

4. 10.26.73.5

−

5. 0.80.2

0.16×

6. 0.60.4

0.24×

7. 0.27

8 2.161 6

56560

−

−

8. 0.52

6 3.123 0

1212

0

−

−



256

9. 9.60.5

4.80×

(9.6)(−0.5) = −4.8

10. 8.70.7

6.09×

(−8.7)(−0.7) = 6.09

11. 123.6048.0475.56

−

12. 325.2036.08

289.12−

13. Subtract absolute values. 25.0000.026

24.974−

Attach the sign of the larger absolute value. −25 + 0.026 = −24.974

14. Subtract absolute values. 44.000

0.12543.875

−

Attach the sign of the larger absolute value. 0.125 + (−44) = −43.875

15. 3.4 29.24 becomes 8.6

34 292.427220 420 4

0

−

−

29.24 ÷ (−3.4) = −8.6

16. 1.9 10.26 becomes 5.4

19 102.6957 67 6

0

−

−

−10.26 ÷ (−1.9) = 5.4

17. −2.8 × 100 = −280

18. 1.6 × 1000 = 1600

19. 96.2107.028

121.700224.938

+

20. 0.2681.930

142.881145.079

+

21. 0.56

46 25.7623 0

2 762 76

0

−

−

−25.76 ÷ −46 = 0.56

22. 0.63

43 27.0925 8

1 291 29

0

−

−

−27.09 ÷ 43 = −0.63


3 601224 008027.6092 3 1 4 decimal places

×

+ =


5 6012140 0300145.6312 3 1 4 decimal places

×

+ =

25. 10.04.65.4

−

26. Subtract absolute values. 18.00

0.2617.74

−

Attach the sign of the greater absolute value. 0.26 − 18 = −17.74



257

27. −268.19 − 146.25 = −268.19 + (−146.25) Add absolute values.

268.19146.25414.44

+


28. −860.18 − 434.85 = −860.18 + (−434.85) Add absolute values.

860.18434.85

1295.03+


29. 0.087 2.958 becomes 34

87 2958261348348

0

−

−

2.958 340.087

= −−

30. 0.061 1.708 becomes 28

61 1708122

488488

0

−

−

1.708 280.061−

= −

31. 160.0043.19

116.81−

32. 120.00101.2118.79

−

33. 15.62 × 10 = 156.2

34. 15.62 ÷ 10 = 1.562

35. 15.6210.0025.62

+

36. 15.6210.00

5.62−

37. 53.779.271.2+

rounds torounds torounds to

508070

200+

The estimated distance is 200 miles.

38. 4.203.300.90

−

It costs $0.90 more to send the package as Priority Mail.

39. 23.3241.556

24.880+

24.88 billion 24.88 1 billion24.88 1,000,000,00024,880,000,000

= ×= ×=

The total amount spent was $24.88 billion or $24,880,000,000.

Section 5.5

Practice Problems

1. a. 0.4

5 2.02.0

0−

2 0.45=

b. 0.225

40 9.0008 01 00

80200200

0

−

−

−

9 0.22540

=



258

2. 0.375

8 3.0002 4

6056

4040

0

−

−

−

3 0.3758

− = −

3. a. 0.833...

6 5.0004 8

2018

20182

−

−

−

5 0.836=

b. 0.22...

9 2.001 8

20182

−

−

2 0.29=

4.

2.1538 2.15413 28.0000

262 01 3

7065

5039110104

6

≈

−

−

−

−

−

5. 5 533

16 16=

3.312516 53.0000

485 04 8

20164032

80800

−

−

−

−

−

Thus, 53 3.3125.

16=

6. 3 3 2 6 0.65 5 2 10= ⋅ = =

7. 3 3 2 6 0.06

50 50 2 100= ⋅ = =

8. 0.2

5 1.01 0

0−

Since 0.2 < 0.25, then 1 0.25.5<

9. a. 1 0.52= and 0.5 < 0.54, so

1 0.54.2<

b. 0.44...

9 4.003 6

40364

−

−

0.4 0.44...,= so 40.4 .9

=



259

c. 0.714

7 5.0004 9

10730282

−

−

−

0.714 < 0.72, so 5 0.72.7<

10. a. 1 0.333...3=

0.302 = 0.302 3 0.3758=

0.302, 1 ,3

38

b. 1.26 = 1.26 11 1.254=

21 1.405=

11 ,4

1.26, 215

c. 0.4 = 0.40 0.41 = 0.41 5 0.717≈

0.4, 0.41, 57

11. 897.8 ÷ 100 × 10 = 8.978 × 10 = 89.78

12. −8.69(3.2 − 1.8) = −8.69(1.4) = −12.166

13. 2( 0.7) 2.1 0.49 2.10 2.59− + = + =

14. 220.06 (1.2) 10 20.06 1.44 10

0.02 0.0220.06 0.144

0.0219.916

0.02995.8

− ÷ − ÷=

−=

=

=

15. 1Area base height21 7 2.120.5 7 2.17.35

= ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅=

The area of the triangle is 7.35 square meters.

16. 1.7y − 2 = 1.7(2.3) − 2 = 3.91 − 2 = 1.91


1. The number 0.5 means 0.555. false

2. To write 9

19 as a decimal, perform the division

19 9. true

3. 2( 1.2)− means (−1.2)(−1.2) or −1.44. false

4. To simplify 8.6(4.8 − 9.6), we first subtract. true

Exercise Set 5.5

1. 0.2

5 1 01.0

0−

1 0.25=

2. 0.05

20 1.001 00

0−

1 0.0520

=

3. 0.68

25 17.0015 0

200200

0

−

−

17 0.6825

=

4. 0.52

25 13.0012 5

5050

0

−

−

13 0.5225

=



260

5. 0.75

4 3.002 8

20200

−

−

3 0.754=

6. 0.375

8 3.0002 4

6056

4040

0

−

−

−

3 0.3758=

7. 0.08

25 2.002 00

0−

2 0.0825

− = −

8. 0.12

25 3.002 5

5050

0

−

−

3 0.1225

− = −

9. 2.25

4 9.0081 0

820200

−

−

−

9 2.254=

10. 1.6

5 8.053 03 0

0

−

−

8 1.65=

11. 0.9166...

12 11.000010 8

20128072

8072

8

−

−

−

−

11 0.91612

=

12. 0.4166...

12 5.00004 8

2012

80728072

8

−

−

−

−

5 0.416

12=

13. 0.425

40 17.00016 01 00

80200200

0

−

−

−

17 0.42540

=

14. 0.76

25 19.0017 5

1 501 50

0

−

−

19 0.7625

=

15. 0.45

20 9.008 01 001 00

0

−

−

9 0.4520

=



261

16. 0.775

40 31.00028 0

3 002 80

200200

0

−

−

−

31 0.77540

=

17. 0.333...

3 1.00091091091

−

−

−

1 0.33

− = −

18. 0.777...

9 7.0006 3

706370637

−

−

−

7 0.79

− = −

19. 0.4375

16 7.00006 4

6048120112

80800

−

−

−

−

7 0.4375

16=

20. 0.5625

16 9.00008 01 00

964032

80800

−

−

−

−

9 0.5625

16=

21.

0.636363...11 7.000000

6 64033

7066

4033

7066

40337

−

−

−

−

−

−

7 0.6311

=

22. 0.8181...

11 9.00008 8

20119088

20119

−

−

−

−

9 0.8111

=

23. 0.85

20 17.0016 0

1 001 00

0

−

−

175 5.8520

=



262

24. 0.875

8 7.0006 4

6056

4040

0

−

−

−

74 4.8758=

25. 0.624

125 78.00075 0

3 002 50

500500

0

−

−

−

78 0.624

125=

26. 0.424

375 159.000150 0

9 007 501 5001 500

0

−

−

−

159 0.424375

=

27. 1 0.333 0.333

− = − ≈ −

28. 7 0.777 0.789

− = − ≈ −

29. 7 0.4375 0.44

16= ≈

30. 9 0.5625 0.56

16= ≈

31. 7 0.6363 0.611

= ≈

32. 9 0.8181 0.811

= ≈

33. 0.615 0.62

91 56.00054 61 40

9149045535

≈

−

−

−

34. 0.42

50 21.0020 01 001 00

0

−

−

35. 0.712 0.71

94 67.00065 81 20

9426018872

≈

−

−

−

36. 0.175

40 7.0004 03 002 80

200200

0

−

−

−

37. 0.02

50 1.001 00

0−

38. 0.00000125

800,000 1.000000008000002000000160000040000004000000

0

−

−

−



263

39. 0.562 0.569 ↑ ↑ 2 < 9 so, 0.562 < 0.569

40. 0.983 0.988 ↑ ↑ 3 < 8 so 0.983 < 0.988

41. 0.215

200 43.00040 0

3 002 001 0001 000

0

−

−

−

430.215200

=

42. 0.725

40 29.00028 01 00

80200200

0

−

−

−

29 0.72540

=

43. 0.0932 0.0923 ↑ ↑ 3 > 2 so, 0.0932 > 0.0923 Thus, −0.0932 < −0.0923.

44. 0.00563 0.00536 ↑ ↑ 6 > 3 so, 0.00563 > 0.00536 Thus, −0.00563 < −0.00536.

45. 0.833...

6 5.0004 8

2018

20182

−

−

−

5 0.836= and 0.6 0.83,< so

50.66

<

46. 0.117 0.12

17 2.0001 7

3017130119

11

≈

−

−

−

2 0.1217

≈ and 0. 1 0.12,< so 20. 1 .

17<

47. 0.5604 0.560

91 51.000045 5

55054640

0400364

36

≈

−

−

−

−

51 0.56091

≈ and 0.560 0.564,< so 51 0.564.91

<

48. 0.5454...

11 6.00005 5

5044

60555044

6

−

−

−

−

6 0.5411

= and 0.583 0.54,> so 60.583 .

11>



264

49. 0.571 0.57

7 4.0003 5

50491073

≈

−

−

−

4 0.577≈ and 0.57 > 0.14, so

4 0.14.7>

50. 0.555...

9 5.0004 5

5045

5045

5

−

−

−

5 0.5559= and 0.555 0.557,< so

5 0.557.9<

51.

1.3846 1.38513 18.0000

135 03 91101 04

6052

80782

≈

−

−

−

−

−

18 1.38513

≈ and 1.38 < 1.385, so 181.38 .13

<

52.

0.37288 0.372959 22.00000

17 74 304 13

170118

520472480472

8

≈

−

−

−

−

−

22 0.372959

≈ and 0.372 < 0.3729, so

220.372 .59

<

53. 7.125

64 456.000448

8 06 41 601 28

320320

0

−

−

−

−

456 7.12564

= and 7.123 < 7.125, so

4567.123 .64

<



265

54.

12.7142 12.7147 89.0000

719145 04 9

1073028

2014

6

≈

−

−

−

−

−

−

89 12.7147≈ and 12.713 < 12.714, so

8912.713 .7

<

55. 0.32, 0.34, 0.35

56. 0.40, 0.42, 0.47

57. 0.49 = 0.490 0.49, 0.491, 0.498

58. 0.72 = 0.720 0.72, 0.727, 0.728

59. 42 5.258=

5.23, 42 ,8

5.34

60. 7.56 = 7.560 67 7.444...9=

7.562 = 7.562 67 ,9

7.56, 7.562

61. 5 0.6258=

0.612, 5 ,8

0.649

62. 5 0.8336=

0.821, 5 ,6

0.849

63. 2(0.3) 0.5 0.09 0.5 0.59+ = + =

64. (−2.5)(3) − 4.7 = −7.5 − 4.7 = −12.2

65. 1 0.8 1.8 18 3

0.6 0.6 6+

= = = −− − −

66. 2( 0.05) 3.13 0.0025 3.13 3.1325− + = + =

67. 2 2( 2.3) (0.3 0.7) ( 2.3) (1.0)5.29(1.0)5.29

− + = −==

68. (8.2)(100) − (8.2)(10) = 820 − 82 = 738

69. (5.6 − 2.3)(2.4 + 0.4) = (3.3)(2.8) = 9.24

70. 0.222 2.13 1.908 0.159

12 12− −

= = −

71. 2(4.5) 20.25 0.2025

100 100= =

72. 0.9(5.6 − 6.5) = 0.9(−0.9) = −0.81

73. 7 0.74 7.74 1.29

6 6+

= = −− −

74. 2(1.5) 0.5 2.25 0.5 2.75+ = + =

75. 1 12(7.8) 15.6 0.2 15.6 15.45 5− = − = − = −

76. 3 3(9.6)(5) 48 0.75 48 47.254 4− = − = − = −

77. 1 1( 9.6 5.2) ( 14.8) 0.25( 14.8) 3.74 4− − = − = − = −

78. 3 3(4.7 5.9) ( 1.2) 0.375( 1.2) 0.458 8

− = − = − = −



266

79. 1Area21 (5.7)(9)20.5(5.7)(9)25.65 square inches

b h= ⋅ ⋅

=

==

80. 1Area21 17 4.420.5 17 4.437.4 square feet

b h= ⋅ ⋅

= ⋅ ⋅

= ⋅ ⋅=

81. Area2(0.62)5

(0.62)(0.4)0.248 square yard

l w= ⋅⎛ ⎞= ⎜ ⎟⎝ ⎠

==

82. Area7(1.2)8

(1.2)(0.875)1.05 square miles

l w= ⋅⎛ ⎞= ⎜ ⎟⎝ ⎠

==

83. 2 2( 2.4) 5.76z = − =

84. 2 2(0.3) 0.09y = =

85. x − y = 6 − 0.3 = 5.7

86. x − z = 6 − (−2.4) = 6 + 2.4 = 8.4

87. 4y − z = 4 ⋅ 0.3 − (−2.4) = 1.2 + 2.4 = 3.6

88. 62 2( 2.4) 20 4.8 15.2

0.3x zy+ = + − = − =

89. 9 16 9 5 16 2 45 32 77

10 25 10 5 25 2 50 50 50+ = ⋅ + ⋅ = + =

90. 4 19 4 2 19 8 19 11 1

11 22 11 2 22 22 22 22 2− = ⋅ − = − = − = −

91. 22 5 2 5 5 2 5 5 5

5 2 5 2 2 5 2 2 2⋅ ⋅⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞⎛ ⎞= = =⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⋅ ⋅⎝ ⎠⎝ ⎠ ⎝ ⎠⎝ ⎠⎝ ⎠

92. 2 32 3 2 2 3 3 3

3 2 3 3 2 2 22 2 3 3 33 3 2 2 232

⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎛ ⎞= ⋅ ⋅ ⋅⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎝ ⎠

⋅ ⋅ ⋅ ⋅=

⋅ ⋅ ⋅ ⋅

=

93. 1.0 = 1

94. 1.0000 = 1

95. 1.00001 > 1

96. 101 > 99, so 101 199

>

97. 99 < 100, so 99 1

100<

98. 99 199

=

99. 0.1889 0.189

10,661 2014.00001066 1

947 90852 8895 02085 288

9 73209 5949

1371

≈

−

−

−

−

2014 0.18910,661

≈

100. 0.124 0.12

10,661 1324.0001066 1257 90213 22

44 68042 6442 036

≈

−

−

−

1324 0.1210,661

≈



267

101. 2019 rounds to 20001324 rounds to 1300

773 rounds to 800684 rounds to 700703 rounds to 700502 rounds to 500

6000

The total number of stations is estimated to be 6000.

102. 0.562 0.56

10,661 6000.0005330 5

669 50639 6629 84021 3228 518

≈

−

−

−

6000 0.5610,661

≈



Section 5.6

Practice Problems

1. 0.9 1.30.9 0.9 1.3 0.9

0.4

zz

z

+ =+ − = −

=

2. 0.17 0.340.17 0.340.17 0.17

2

xx

x

= −−

=

= −

3. 2.9 1.7 0.32.9 1.7 1.7 0.3 1.7

1.2 0.31.2 0.30.3 0.3

4

xx

xx

x

= +− = + −

=

=

=

4. 8 4.2 10 11.68 4.2 4.2 10 11.6 4.2

8 10 7.48 10 10 10 7.4

2 7.42 7.42 2

3.7

x xx x

x xx x x x

xx

x

+ = ++ − = + −

= +− = − +− =−

=− −

= −

5. 6.3 5 3( 2.9)6.3 5 3 8.7

6.3 5 6.3 3 8.7 6.35 3 2.4

5 3 3 2.4 38 2.48 2.48 8

0.3

x xx x

x xx x

x x x xxx

x

− = +− = +

− − = + −− = +

− − = + −− =−

=− −

= −

6. 0.2 2.6 410(0.2 2.6) 10(4)

10(0.2 ) 10(2.6) 10(4)2 26 40

2 26 26 40 262 142 142 2

7

yy

yy

yyy

y

+ =+ =

+ =+ =

+ − = −=

=

=

Exercise Set 5.6

1. 1.2 7.11.2 1.2 7.1 1.2

5.9

xx

x

+ =+ − = −

=

2. 0.5 90.5 0.5 9 0.5

9.5

yy

y

− =− + = +

=

3. 5 2.155 2.155 5

0.43

yy

y

− =−

=− −

= −

4. 0.4 500.4 500.4 0.4

125

xx

x

− =−

=− −

= −



268

5. 6.2 46.2 4 4 4

10.2

yyy

= −+ = − +

=

6. 9.7 11.69.7 11.6 11.6 11.6

1.9

xxx

= +− = + −− =

7. 3.1 13.953.1 13.953.1 3.1

4.5

xx

x

= −−

=

= −

8. 3 25.83 25.83 3

8.6

yy

y

= −−

=

= −

9. 3.5 2.8 11.23.5 2.8 2.8 11.2 2.8

3.5 143.5 143.5 3.5

4

xx

xx

x

− + = −− + − = − −

− = −− −

=− −

=

10. 7.1 0.2 6.17.1 0.2 7.1 6.1 7.1

0.2 10.2 10.2 0.2

5

xx

xx

x

− =− − = −

− = −− −

=− −

=

11. 6 8.65 3 106 8.65 8.65 3 10 8.65

6 3 1.356 3 3 3 1.35

3 1.353 1.353 3

0.45

x xx x

x xx x x x

xx

x

+ = ++ − = + −

= +− = − +

=

=

=

12. 7 9.64 5 2.327 9.64 9.64 5 2.32 9.64

7 5 11.967 5 5 5 11.96

2 11.962 11.962 2

5.98

x xx x

x xx x x x

xx

x

− = +− + = + +

= +− = − +

=

=

=

13. 2( 1.3) 5.82 2.6 5.8

2 2.6 2.6 5.8 2.62 8.42 8.42 2

4.2

xx

xxx

x

− =− =

− + = +=

=

=

14. 5( 2.3) 19.55 11.5 19.5

5 11.5 11.5 19.5 11.55 85 85 5

1.6

xx

xxx

x

+ =+ =

+ − = −=

=

=

15. 0.4 0.7 0.910(0.4 0.7) 10( 0.9)

4 7 94 7 7 9 7

4 164 164 4

4

xxx

xxx

x

+ = −+ = −+ = −

+ − = − −= −−

=

= −

16. 0.7 0.1 1.510(0.7 0.1) 10(1.5)

7 1 157 1 1 15 1

7 147 147 7

2

xxx

xxx

x

+ =+ =

+ =+ − = −

=

=

=

17. 7 10.810(7 10.8) 10

70 108 1070 70 108 10 70

108 60108 6060 601.8

x xx xx x

x x x xxx

x

− =− = ⋅− =

− − = −− = −− −

=− −

=

18. 3 7 24.410 3 10(7 24.4)

30 70 24430 70 70 70 244

40 24440 24440 40

6.1

y yy yy y

y y y yyy

y

= +⋅ = +

= +− = − +− =−

=− −

= −



269

19. 2.1 5 1.6 1010(2.1 5 1.6 ) 10 10

21 50 16 1005 50 100

5 50 50 100 505 505 505 5

10

x xx xx x

xx

xx

x

+ − =+ − = ⋅+ − =

+ =+ − = −

=

=

=

20. 1.5 2 1.2 12.210(1.5 2 1.2 ) 10 12.2

15 20 12 1223 20 122

3 20 20 122 203 1023 1023 3

34

x xx xx x

xx

xx

x

+ − =+ − = ⋅+ − =

+ =+ − = −

=

=

=

21. 3.6 43.6 3.6 4 3.6

7.6

yy

y

− =− + = +

=

22. 5.7 8.45.7 5.7 8.4 5.7

2.7

xx

x

+ =+ − = −

=

23. 0.02 1.20.02 1.20.02 0.02

60

xx

x

− = −− −

=− −

=

24. 9 0.1629 0.1629 9

0.018

yy

y

− = −− −

=− −

=

25. 6.5 10 7.26.5 7.2 10 7.2 7.2

0.7 100.7 1010 100.07

xxxx

x

= +− = + −− =−

=

− =

26. 2 4.2 8.62 4.2 4.2 8.6 4.2

2 12.82 12.82 2

6.4

xx

xx

x

− =− + = +

=

=

=

27. 2.7 25 1.2 52.7 25 25 1.2 5 25

2.7 1.2 302.7 1.2 1.2 1.2 30

1.5 301.5 301.5 1.5

20

x xx x

x xx x x x

xx

x

− = +− + = + +

= +− = − +

=

=

=

28. 9 6.9 6 11.19 6.9 6.9 6 11.1 6.9

9 6 4.29 6 6 6 4.2

3 4.23 4.23 3

1.4

y yy y

y yy y y y

yy

y

− = −− + = − +

= −− = − −

= −−

=

= −

29. 200 0.67 100 0.81200 0.67 0.67 100 0.81 0.67

200 100 1.48200 100 100 100 1.48

100 1.48100 1.48100 100

0.0148

x xx x

x xx x x x

xx

x

− = +− + = + +

= +− = − +

=

=

=

30. 2.3 500 600 0.22.3 2.3 500 600 0.2 2.3

500 600 2.5500 600 600 600 2.5

100 2.5100 2.5100 100

0.025

x xx xx x

x x x xxx

x

+ = −− + = − −

= −− = − −− = −− −

=− −

=

31. 3( 2.71) 23 8.13 2

3 3 8.13 2 38.138.13

1 18.13

x xx x

x x x xxx

x

+ =+ =

− + = −= −−

=− −

− =

32. 7( 8.6) 67 60.2 6

7 7 60.2 6 760.260.2

1 160.2

x xx x

x x x xxx

x

+ =+ =

− + = −= −−

=− −

− =



270

33. 8 5 10 88 5 8 10 8 8

8 3 108 3 8 10 8

3 23 22 2

1.5

x xx xx x

x x x xxx

x

− = −− + = − +

+ =+ − = −

=

=

=

34. 24 10 20 1724 10 10 20 17 10

24 20 724 20 20 20 7

4 74 74 4

1.75

y yy y

y yy y y y

yy

y

− = −− + = − +

= −− = − −

= −−

=

= −

35. 1.2 0.3 0.91.2 0.3 1.2 0.9 1.2

0.3 0.30.3 0.30.3 0.3

1

xx

xx

x

+ =+ − = −

= −−

=

= −

36. 1.5 0.4 0.51.5 0.5 0.4 0.5 0.5

1 0.41 0.4

0.4 0.42.5

xxxx

x

= +− = + −

=

=

=

37. 0.9 2.65 0.5 5.45100( 0.9 2.65) 100( 0.5 5.45)

90 265 50 54590 265 90 50 545 90

265 40 545265 545 40 545 545

280 40280 4040 40

7

x xx xx x

x x x xxxxx

x

− + = − +− + = − +− + = − +

− + + = − + += +

− = + −− =−

=

− =

38. 50 0.81 40 0.48100( 50 0.81) 100( 40 0.48)

5000 81 4000 485000 81 48 4000 48 48

5000 129 40005000 5000 129 4000 5000

129 1000129 10001000 10000.129

x xx xx x

x xx x

x x x xxx

x

− + = − −− + = − −− + = − −

− + + = − − +− + = −

− + + = − +=

=

=

39. 4 7.6 2(3 3.2)4 7.6 6 6.4

10(4 7.6) 10(6 6.4)40 76 60 64

40 76 64 60 64 6440 140 60

40 40 140 60 40140 20140 2020 20

7

x xx xx xx x

x xx x

x x x xxx

x

+ = −+ = −+ = −+ = −

+ + = − ++ =

− + = −=

=

=

40. 4(2 1.6) 5 6.48 6.4 5 6.4

8 6.4 6.4 5 6.4 6.48 5

8 5 5 53 03 03 3

0

x xx x

x xx x

x x x xxx

x

− = −− = −

− + = − +=

− = −=

=

=

41. 0.7 13.8 2.16100(0.7 13.8) 100( 2.16)

70 1380 100 21670 1380 216 100 216 216

70 1596 10070 1596 70 100 70

1596 301596 30

30 3053.2

x xx xx x

x xx x

x x x xxx

x

+ = −+ = −+ = −

+ + = − ++ =

+ − = −=

=

=



271

42. 5 0.3 4.110( 5) 10(0.3 4.1)10 50 3 41

10 50 50 3 41 5010 3 91

10 3 3 3 917 917 917 7

13

y yy yy y

y yy y

y y y yyy

y

− = +− = +− = +

− + = + += +

− = − +=

=

=

43. 2x − 7 + x − 9 = (2x + x) + (−7 − 9) = 3x − 16

44. x + 14 − 5x − 17 = (x − 5x) + (14 − 17) = −4x − 3

45. 2 26 1 6 1 2 3 35 5 2 52 5 2x x x

x x xx x⋅ ⋅ ⋅

⋅ = = =⋅ ⋅ ⋅⋅

46. 2 7 2 3

3 7 3 7 7 37 621 217 6

211321

x x x x

x x

x x

x

+ = ⋅ + ⋅

= +

+=

=

47. 1 1 16 55 16 6 16 2 3 325 93 6 3 6 3 55 3 55 55

⋅ ⋅÷ = ÷ = ⋅ = =

⋅

48. 9 13 9 450 14 49 14 35

13 13 13 13− = − =

49. 4.6 8.34.6 4.6 8.3 4.6

3.7

bb

b

+ =+ − = −

=

50. 15.9 3.815.9 15.9 3.8 15.9

12.1

yy

y

− = −− + = − +

=

51. 2 0.6 4 0.01 2 4 0.6 0.016 0.61

x x x xx

− + − = + − −= −

52. 4.1 4.02 4.1 4.022 8.12

x x x xx

− − − − = − − − −= − −

53. 5 1.2 7 8 5 7 1.2 82 6.8

y y y yy

− − + = − − += − +

54. 9 5.6 3 6 9 3 5.6 6 6 0.4a a a a a− − + = − − + = +

55. 2.8 6.32.8 6.3 6.3 6.3

9.1

zzz

= −+ = − +

=

56. 9.7 4.39.7 4.3 4.3 4.3

5.4

xxx

= +− = + −

=

57. 4.7 8.3 5.84.7 8.3 8.3 5.8 8.3

4.7 14.14.7 14.14.7 4.7

3

xx

xx

x

+ = −+ − = − −

= −−

=

= −

58. 2.8 3.4 13.42.8 3.4 3.4 13.4 3.4

2.8 16.82.8 16.82.8 2.8

6

xx

xx

x

+ = −+ − = − −

= −−

=

= −

59. 7.76 8 12 8.91 8 12 7.76 8.914 16.67

z z z zz

+ − + = − + += − +

60. 9.21 4 11.33 4 9.21 11.333 20.54

x x x xx

+ − + = − + += − +

61. 5( 3.14) 45 5 3.14 4

5 15.7 45 5 15.7 4 5

15.715.7

x xx xx x

x x x xxx

− =⋅ − ⋅ =

− =− − = −

− = −=

62. 6( 1.43) 56 8.58 5

6 6 8.58 5 68.588.58

x xx x

x x x xxx

+ =+ =

− + = −= −

− =

63. 2.6 8.3 4.6 3.410(2.6 8.3) 10(4.6 3.4)

26 83 46 3426 83 83 46 34 83

26 46 11726 46 46 46 117

20 11720 11720 20

5.85

y yy yy y

y yy y

y y y yyy

y

+ = −+ = −+ = −

+ − = − −= −

− = − −− = −− −

=− −

=



272

64. 8.4 2.6 5.4 10.310(8.4 2.6) 10(5.4 10.3)

84 26 54 10384 26 26 54 103 26

84 54 12984 54 54 54 129

30 12930 12930 30

4.3

z zz zz z

z zz z

z z z zzz

z

− = +− = +− = +

− + = + += +

− = − +=

=

=

65. 9.6 3.2 11.7 6.9 9.6 11.7 3.2 6.92.1 10.1

z z z zz

− − − = − − −= − −

66. 3.2 12.6 8.9 15.23.2 8.9 12.6 15.212.1 2.6

x xx xx

− + − −= − − + −= − −



69. 5.25 40.335755.25 40.335755.25 5.25

7.683

xx

x

− = −− −

=− −

=

70. 7.68 114.984967.68 114.984967.68 7.68

14.972

yy

y

= −−

=

= −

71. 1.95 6.834 7.65 19.85911.95 6.834 6.834 7.65 19.8591 6.834

1.95 7.65 26.69311.95 7.65 7.65 7.65 26.6931

5.7 26.69315.7 26.69315.7 5.7

4.683

y yy y

y yy y y y

yy

y

+ = −+ − = − −

= −− = − −− = −− −

=− −

=

72. 6.11 4.683 7.51 18.2356.11 4.683 4.683 7.51 18.235 4.683

6.11 7.51 13.5526.11 7.51 7.51 7.51 13.552

1.4 13.5521.4 13.5521.4 1.4

9.68

x xx x

x xx x x x

xx

x

+ = ++ − = + −

= +− = − +− =−

=− −

= −

Section 5.7

Practice Problems

1. 87 75 96 91 78 427Mean 85.4

5 5+ + + +

= = =

2. 4 2 3 4 2 5 1 2 4 2 40gpa 2.67

2 4 5 2 2 15⋅ + ⋅ + ⋅ + ⋅ + ⋅

= = ≈+ + + +

3. Because the numbers are in numerical order, the median is the middle number, 24.

4. Write the numbers in numerical order: 36, 65, 71, 78, 88, 91, 95, 95 The median is the mean of the two middle numbers.

78 88median 832+

= =

5. Mode: 15 because it occurs most often, 3 times.

6. Median: Write the numbers in order. 15, 15, 15, 16, 18, 26, 26, 30, 31, 35 Median is mean of middle two numbers, 18 26 22.

2+

=

Mode: 15 because it occurs most often, 3 times.


1. Another word for “mean” is average.

2. The number that occurs most often in a set of numbers is called the mode.

3. The mean (or average) of a set of number items

is sum of items .

number of items

4. The median of a set of numbers is the middle number. If the number of numbers is even, it is the mean (or average) of the two middle numbers.

5. An example of weighted mean is a calculation of grade point average.



273

Exercise Set 5.7

1. Mean: 15 23 24 18 25 105 21

5 5+ + + +

= =

Median: Write the numbers in order: 15, 18, 23, 24, 25 The middle number is 23. Mode: There is no mode, since each number occurs once.

2. Mean: 45 36 28 46 52 207 41.4

5 5+ + + +

= =

Median: Write the numbers in order: 28, 36, 45, 46, 52 The middle number is 45. Mode: There is no mode, since each number occurs once.

3. Mean: 7.6 8.2 8.2 9.6 5.7 9.1 48.4 8.1

6 6+ + + + +

= ≈

Median: Write the numbers in order: 5.7, 7.6, 8.2, 8.2, 9.1, 9.6

Median is mean of middle two: 8.2 8.2 8.2

2+

=

Mode: 8.2 since this number appears twice.

4. Mean: 4.9 7.1 6.8 6.8 5.3 4.9 35.8 6.0

6 6+ + + + +

= ≈

Median: Write the numbers in order: 4.9, 4.9, 5.3, 6.8, 6.8, 7.1

Median is mean of middle two: 5.3 6.8 6.05

2+

=

Mode: Since 6.8 and 4.9 occur twice, there are two modes, 6.8 and 4.9.

5. Mean: 0.5 0.2 0.2 0.6 0.3 1.3 0.8 0.1 0.5

94.59

0.5

+ + + + + + + +

=

=

Median: Write the numbers in order: 0.1, 0.2, 0.2, 0.3, 0.5, 0.5, 0.6, 0.8, 1.3 The middle number is 0.5. Mode: Since 0.2 and 0.5 occur twice, there are two modes, 0.2 and 0.5.

6. Mean: 0.6 0.6 0.8 0.4 0.5 0.3 0.7 0.8 0.1

94.89

0.5

+ + + + + + + +

=

≈

Median: Write the numbers in order: 0.1, 0.3, 0.4, 0.5, 0.6, 0.6, 0.7, 0.8, 0.8 The middle number is 0.6. Mode: Since 0.6 and 0.8 occur twice, there are two modes, 0.6 and 0.8.

7. Mean: 231 543 601 293 588 109 334 268

82967

8370.9

+ + + + + + +

=

≈

Median: Write the numbers in order: 109, 231, 268, 293, 334, 543, 588, 601

The mean of the middle two: 293 334 313.5

2+

=

Mode: There is no mode, since each number occurs once.

8. Mean: 451 356 478 776 892 500 467 780

84700

8587.5

+ + + + + + +

=

=

Median: Write the numbers in order: 356, 451, 467, 478, 500, 776, 780, 892

The mean of the middle two: 478 500 489

2+

=

Mode: There is no mode, since each number occurs once.

9. Mean: 1679 1483 1483 1450 1380 7475

5 51495 feet

+ + + +=

=

10. Because the numbers are in numerical order, the median height is the middle number (of the top 5), 1483 feet.

11. Because the numbers are in numerical order, the median is mean of the middle two (of the top 8), 1450 1380 1415 feet.

2+

=



274

12. Mean: 1679 1483 1483 1450 1380 1362 1283 1260 11,380 1422.5 feet

8 8+ + + + + + +

= =


14. answer may vary

15. 3 3 2 3 4 4 2 4 39gpa 2.79

3 3 4 4 14⋅ + ⋅ + ⋅ + ⋅

= = ≈+ + +

16. 1 1 0 1 2 4 3 5 24gpa 2.18

1 1 4 5 11⋅ + ⋅ + ⋅ + ⋅

= = ≈+ + +

17. 4 3 4 3 4 4 3 3 2 1gpa

3 3 4 3 151143.64

⋅ + ⋅ + ⋅ + ⋅ + ⋅=

+ + + +

=

≈

18. 3 2 3 2 2 3 4 3 3 3 39gpa 3.0

2 2 3 3 3 13⋅ + ⋅ + ⋅ + ⋅ + ⋅

= = =+ + + +

19. Mean: 7.8 6.9 7.5 4.7 6.9 7.0 40.8 6.8

6 6+ + + + +

= =

20. Median: Write the numbers in order. 4.7, 6.9, 6.9, 7.0, 7.5, 7.8

The mean of the middle two: 6.9 7.0 6.95

2+

=

21. Mode: 6.9, since this number appears twice.

22. Mean: 93 85 89 79 88 91 525 87.5

6 6+ + + + +

= =

23. Median: Write the numbers in order. 79, 85, 88, 89, 91, 93


2+

=

24. Mode: There is no mode, since each number occurs only once.

25. Mean: sum of 15 pulse rates 1095 73

15 15= =

26. Median: Write the numbers in order. 64, 65, 66, 68, 70, 70, 71, 71, 72, 75, 77, 78, 80, 82, 86 The middle number is 71.

27. Mode: Since 70 and 71 occur twice, there are two modes, 70 and 71.

28. There were 6 pulse rates higher than the mean. They are 75, 77, 78, 80, 82, and 86.



275

29. There were 9 rates lower than the mean. They are 66, 68, 71, 64, 71, 70, 65, 70, and 72.

30. 12 4 3 320 4 5 5

⋅= =

⋅

31. 6 1 6 1

18 3 6 3⋅

= =⋅

32. 4 436 4 9 9x x x⋅= =

⋅

33. 18 3 6 3

30 5 6 5y y y⋅

= =⋅ ⋅

34. 3

235 5 7 7

5 20 20100a a a a a

a aa⋅ ⋅ ⋅ ⋅

= =⋅ ⋅ ⋅

35. 2

255 5 11 11

5 15 1575y y y

y yy⋅ ⋅ ⋅

= =⋅ ⋅ ⋅

36. Since the mode is 21, 21 must occur at least twice in the set. Since there are an odd number of numbers in the set, the median, 20 is in the set. Therefore the missing numbers are 20, 21, 21.

37. Since the mode is 35, 35 must occur at least twice in the set. Since there are an odd number of numbers in the set, the median, 37 is in the set. Let n be the remaining unknown number.

Mean: 35 35 37 40 38

5147 38

51475 5 38

5147 190

147 147 190 14743

n

n

n

nnn

+ + + +=

+=

+⋅ = ⋅

+ =− + = −

=

The missing numbers are 35, 35, 37, and 43.


39. yes; answers may vary

Chapter 5 Vocabulary Check

1. Like fractional notation, decimal notation is used to denote a part of a whole.

2. To write fractions as decimals, divide the numerator by the denominator.

3. To add or subtract decimals, write the decimals so that the decimal points line up vertically.

4. When writing decimals in words, write “and” for the decimal point.

5. When multiplying decimals, the decimal point in the product is placed so that the number of decimal places in the product is equal to the sum of the number of decimal places in the factors.

6. The mode of a set of numbers is the number that occurs most often.

7. The distance around a circle is called the circumference.

8. The median of a set of numbers in numerical order is the middle number. If there are an even number of numbers, the mode is the mean of the two middle numbers.

9. The mean of a list of number items is sum of items .

number of items

10. When 2 million is written as 2,000,000, we say it is written in standard form.

Chapter 5 Review

1. In 23.45, the 4 is in the tenths place.

2. In 0.000345, the 4 is in the hundred-thousandths place.

3. −23.45 in words is negative twenty-three and forty-five hundredths.

4. 0.00345 in words is three hundred forty-five hundred-thousandths.

5. 109.23 in words is one hundred nine and twenty-three hundredths.

6. 200.000032 in words is two hundred and thirty-two millionths.

7. Eight and six hundredths is 8.06.



276

8. Negative five hundred three and one hundred two thousandths is −503.102.

9. Sixteen thousand twenty-five and fourteen ten-thousandths is 16,025.0014.

10. Fourteen and eleven thousandths is 14.011.

11. 16 40.16100 25

= =

12. 2312.023 12

1000− = −

13. 231 0.00231

100,000=

14. 1 2525 25 25.254 100= =

15. 0.49 0.43 ↑ ↑ 9 > 3 so 0.49 > 0.43

16. 0.973 = 0.9730

17. 38.0027 38.00056 ↑ ↑ 2 > 0 so 38.0027 > 38.00056 Thus, −38.0027 < −38.00056.

18. 0.230505 0.23505 ↑ ↑ 0 < 5 so 0.23050 < 0.23505 Thus, −0.230505 > −0.23505.

19. To round 0.623 to the nearest tenth, observe that the digit in the hundredths place is 2. Since this digit is less than 5, we do not add 1 to the digit in the tenths place. The number 0.623 rounded to the nearest tenth is 0.6.

20. To round 0.9384 to the nearest hundredth, observe that the digit in the thousandths place is 8. Since this digit is at least 5, we add 1 to the digit in the hundredths place. The number 0.9384 rounded to the nearest hundredth is 0.94.

21. To round −42.895 to the nearest hundredth, observe that the digit in the thousandths place is 5. Since this digit is at least 5, we add 1 to the digit in the hundredths place. The number −42.895 rounded to the nearest hundredth is −42.90.


23. 887 million 887 1 million887 1,000,000887,000,000

= ×= ×=

24. 600 thousand 600 1 thousand600 1000600,000

= ×= ×=

25. 8.69.5

18.1+

26. 3.91.25.1

+

27. Add the absolute values. 6.400.887.28

+

Attach the common sign. −6.4 + (−0.88) = −7.28

28. Subtract the absolute values. 19.02

6.9812.04

−


29. 200.49016.820

103.002320.312

+



277

30. 0.00236100.45000

48.29000148.74236

+

31. 4.93.21.7

−

32. 5.232.742.49

−


892.1432.4

1324.5+



10.2000.064

10.136−


35. 100.0034.9865.02

−

36. 200.000000.00198

199.99802−

37. 19.915.110.96.7

52.6+

The total distance is 52.6 miles.

38. x − y = 1.2 − 6.9 = −5.7

39. Perimeter = 6.2 + 4.9 + 6.2 + 4.9 = 22.2 The perimeter is 22.2 inches.

40. Perimeter = 11.8 + 12.9 + 14.2 = 38.9 The perimeter is 38.9 feet.

41. 7.2 × 10 = 72

42. 9.345 × 1000 = 9345

43. A negative number multiplied by a positive number is a negative number.

34.02 2 decimal places2.3 1 decimal place

10 20668 04078.246 2 1 3 decimal places

×

+ =

−34.02 × 2.3 = −78.246

44. A negative number multiplied by a negative number is a positive number.

839.02 2 decimal places87.3 1 decimal place

251 7065873 140

67121 60073246.446 2 1 3 decimal places

×

+ =

−839.02 × (−87.3) = 73,246.446

45. C = 2πr = 2π ⋅ 7 = 14π meters C ≈ 14 ⋅ 3.14 = 43.96 meters

46. C = πd = π ⋅ 20 = 20π inches C ≈ 20 ⋅ 3.14 = 62.8 inches

47. 0.0877

3 0.263124

232121210

−

−

−

48.

15.82520 316.500

2011610016 516 0

5040100100

0

−

−

−

−

−



278


0.3 21 becomes 70

3 2102100

−

−21 ÷ (−0.3) = 70

50. A negative number divided by a positive number is a negative number.

0.03 0.0063 becomes 0.21

3 0.63603

30

−

−

−0.0063 ÷ 0.03 = −0.21

51. 0.34 2.74 becomes 8.0588 8.059

34 274.0000272

2 00

2001 70

300272

280272

8

≈

−

−

−

−

−

52. 19.8 601.92 becomes 30.4

198 6019.2594

790

79 279 2

0

−

−

−

53. 23.65 0.023651000

=

54. 93 9.310

= −−

55. 3.28 24 becomes 7.31 7.3

328 2400.002296104 098 45 603 282 32

≈

−

−

−

There are approximately 7.3 meters in 24 feet.

56. 69.71 3136.95 becomes 45

6971 313695278843485534855

0

−

−

It will take him 45 months to pay off the loan.

57. 0.8

5 4.04 0

0−

4 0.85=

58. 0.9230 0.923

13 12.000011 7

3026

4039100

10

≈

−

−

−

−

12 0.92313

− ≈ −

59. 0.3333...

3 1.0000910

91091091

−

−

−

−

12 2.33= or 2.333



279

60. 0.2166...

60 13.000012 0

1 006040036040036040

−

−

−

−

13 0.21616

= or 0.217

61. 0.392 = 0.392

62. 0.571 0.57

7 4.0003 5

5049

1073

≈

−

−

−

4 0.577≈ and 0.57 < 0.625, so

4 0.625.7<

63. 0.2941 0.294

17 5.00003 41 601 53

7068

2017

3

≈

−

−

−

−

5 0.29417

≈ and 0.293 < 0.294, so 50.293 .

17<

64. 0.0231 0.0221 ↑ ↑ 3 > 2 so 0.0231 > 0.0221, thus −0.0231 < −0.0221.

65. 0.832, 0.837, 0.839

66. 5 0.6258=

5 ,8

0.626, 0.685

67. 3 0.4287≈

0.42, 3 ,7

0.43

68. 18 1.636311

=

1.63 = 1.63 19 1.58312

=

19 ,12

1.63, 1811

69. −7.6 × 1.9 + 2.5 = −14.44 + 2.5 = −11.94

70. 2( 2.3) 1.4 5.29 1.4 3.89− − = − =

71. 7 0.74 7.74 129

0.06 0.06+

= = −− −

72. 0.9(6.5 − 5.6) = 0.9(0.9) = 0.81

73. 2(1.5) 0.5 2.25 0.5 2.75 55

0.05 0.05 0.05+ +

= = =

74. 0.0726 ÷ 10 × 1000 = 0.00726 × 1000 = 7.26

75. 1Area21 (4.6)(3)20.5(4.6)(3)6.9 square feet

b h= ⋅ ⋅

=

==

76. 1Area21 (5.2)(2.1)20.5(5.2)(2.1)5.46 square inches

b h= ⋅ ⋅

=

==

77. 3.9 4.23.9 3.9 4.2 3.9

0.3

xx

x

+ =+ − = −

=



280

78. 70 22.8170 22.81 22.81 22.81

92.81

yyy

= −+ = − +

=

79. 2 17.22 17.22 2

8.6

xx

x

=

=

=

80. 1.1 881.1 881.1 1.1

80

yy

y

− =−

=− −

= −

81. 3 0.78 1.2 23 0.78 0.78 1.2 2 0.78

3 1.98 23 2 1.98 2 2

1.98

x xx x

x xx x x x

x

− = +− + = + +

= +− = + −

=

82. 0.6 2 4 0.93 0.6 4 0.9

3 0.6 0.6 4 0.9 0.63 4 1.5

3 4 4 4 1.51.5

x x xx x

x xx x

x x x xx

− + − = − −− + = − −

− + − = − − −− = − −

− + = − + −= −

83. 1.3 9.4 0.4 8.610( 1.3 9.4) 10( 0.4 8.6)

13 94 4 8613 94 94 4 86 94

13 4 18013 4 4 4 180

9 1809 1809 9

20

x xx xx x

x xx x

x x x xxx

x

− − = − +− − = − +− − = − +

− − + = − + +− = − +

− + = − + +− =−

=− −

= −

84. 3( 1.1) 5 5.33 3.3 5 5.3

3 3.3 3.3 5 5.3 3.33 5 2

3 5 5 5 22 22 22 2

1

x xx x

x xx x

x x x xxx

x

− = −− = −

− + = − += −

− = − −− = −− −

=− −

=



281

85. Mean: 13 23 33 14 6 89 17.8

5 5+ + + +

= =

Median: Write the numbers in order. 6, 13, 14, 23, 33 The middle number is 14. Mode: There is no mode, since each number occurs once.

86. 45 86 21 60 86 64 45Mean

74077

58.1

+ + + + + +=

=

≈

Median: Write the numbers in order. 21, 45, 45, 60, 64, 86, 86 The middle number is 60. Mode: There are 2 numbers that occur twice, so there are two modes, 45 and 86.

87. 14,000 20,000 12,000 20,000 36,000 45,000 147,000Mean 24,500

6 6+ + + + +

= = =

Median: Write the numbers in order. 12,000, 14,000, 20,000, 20,000, 36,000, 45,000

The mean of the middle two: 20,000 20,000 20,000

2+

=

Mode: 20,000 is the mode because it occurs twice.

88. 560 620 123 400 410 300 400 780 430 450 4473Mean 447.3

10 10+ + + + + + + + +

= = =

Median: Write the numbers in order. 123, 300, 400, 400, 410, 430, 450, 560, 620, 780

The mean of the two middle numbers: 410 430 420

2+

=

Mode: 400 is the mode because it occurs twice.

89. 4 3 4 3 2 2 3 3 2 1 39gpa 3.25

3 3 2 3 1 12⋅ + ⋅ + ⋅ + ⋅ + ⋅

= = =+ + + +

90. 3 3 3 4 2 2 1 2 3 3 36gpa 2.57

3 4 2 2 3 14⋅ + ⋅ + ⋅ + ⋅ + ⋅

= = ≈+ + + +

91. 200.0032 in words is two hundred and thirty-two ten thousandths.

92. Negative sixteen and nine hundredths is −16.09 in standard form.

93. 8470.0847

10,000=



282

94. 6 0.8577≈

8 0.8899≈

0.75 = 0.750

0.75, 6 8,7 9

95. 7 0.07

100− = −

96. 0.1125

80 9.00008 01 00

80200160

400400

0

−

−

−

−

9 0.1125

80=

97.

51.0571 51.057175 8935.0000

875185175

1000

10008751 2501 225

250175

75

≈

−

−

−

−

−

−

8935 51.057175

≈

98. 402.000032 402.00032 ↑ ↑ 0 < 3 so 402.000032 < 402.00032 Thus, −402.000032 > −402.00032.

99. 6 0.54

11=

0.54 0.55,< so 6 0.55

11<

100. To round 86.905 to the nearest hundredth, observe that the digit in the thousandths place is 5. Since this digit is at least 5, we add 1 to the digit in the hundredths place. The number 86.905 rounded to the nearest hundredth is 86.91.


102. To round 123.46 to the nearest one, observe that the digit in the tenths place is 4. Since this digit is less than 5, we do not add 1 to the digit in the ones place. The number $123.46 rounded to the nearest dollar (or one) is $123.00.

103. To round 3645.52 to the nearest one, observe that the digit in the tenths place is 5. Since this digit is at least 5, we add 1 to the digit in the ones place. The number $3645.52 rounded to the nearest dollar (or one) is $3646.00.

104. Subtract absolute values. 4.93.21.7

−


105. 9.123.865.26

−

106. Subtract absolute values. 102.0689.3012.76

−

Attach the sign of the larger absolute value. −102 + 89.3 = −12.76

107. 4.02110.830

( ) 0.05614.907

−−

+ −−



283

108. 2.54 2 decimal places3.2 1 decimal place508


×

+ =


3456 9007.245 2 1 3 decimal places

−×

− + =

110. 0.005 24.5 becomes 4900

5 2450020

4545000

−

−

111. 2.3 54.98 becomes 23.9043 23.904

23 549.800046896920 820 7

100

10092

806911

≈

−

−

−

−

−

−

112. length = 115.9 ≈ 120 width = 77.3 ≈ 80 Area length width

120 809600 square feet

= ⋅= ⋅=

113. $1.89$1.07$0.99

rounds torounds torounds to

$2$1$1$4

Yes, the items can be purchased with a $5 bill.

114. 2(3.2) 10.24 0.1024

100 100= =

115. (2.6 + 1.4)(4.5 − 3.6) = (4)(0.9) = 3.6

116. Mean: 73 82 95 68 54 372 74.4

5 5+ + + +

= =

Median: Write the numbers in order. 54, 68, 73, 82, 95 The median is the middle value: 73. Mode: There is no mode, since each number occurs once.

117. Mean: 952 327 566 814 327 729 3715

6 6619.17

+ + + + +=

≈

Median: Write the numbers in order. 327, 327, 566, 729, 814, 952 The mean of the two middle values: 566 729 647.5

2+

=

Mode: 327, since this number appears twice.

Chapter 5 Test

1. 45.092 in words is forty-five and ninety-two thousandths.

2. Three thousand and fifty-nine thousandths in standard form is 3000.059.

3. 2.8934.210

10.49217.595

+

4. Add the absolute values. 47.92

3.2851.20

+


5. Subtract the absolute values. 30.25

9.8320.42

−



40 80040.902 1 2 3 decimal places

×

+ =



284

7. 0.23 0.00843 becomes 0.0366 0.036

23 0.843069153138

15013812

≈

−

−

−

(−0.00843) ÷ (−0.23) ≈ 0.037

8. 34.8923 rounded to the nearest tenth is 34.9.

9. 0.8623 rounded to the nearest thousandth is 0.862.

10. 25.0909 25.9090 ↑ ↑ 0 < 9 so 25.0909 < 25.9090

11. 0.444...

9 4.0003 6

4036

40364

−

−

−

0.444 0.445,< so 4 0.445.9<

12. 345 5 69 690.345

1000 5 200 200⋅

= = =⋅

13. 7324.73 24

100− = −

14. 13 1 13 1 1 5 5 0.526 2 13 2 2 5 10

⋅ ⋅− = − = − = − = − = −

⋅ ⋅

15. 0.9411 0.941

17 16.000015 3

7068

2017

301713

≈

−

−

−

−

16 0.94117

≈

16. 2( 0.6) 1.57 0.36 1.57 1.93− + = + =

17. 0.23 1.63 1.86 6.2

0.3 0.3+

= = −− −

18. 2.4 3.6 1.9 9.8(2.4 1.9 ) ( 3.6 9.8)0.5 13.4

x xx xx

− − −= − + − −= −

19. 0.2 1.3 0.70.2 1.3 1.3 0.7 1.3

0.2 0.60.2 0.60.2 0.2

3

xx

xx

x

+ =+ − = −

= −−

=

= −

20. 2( 5.7) 6 3.42 11.4 6 3.4

2 11.4 11.4 6 3.4 11.42 6 14.8

2 6 6 6 14.84 14.84 14.84 4

3.7

x xx x

x xx x

x x x xxx

x

+ = −+ = −

+ − = − −= −

− = − −− = −− −

=− −

=

21. Mean: 26 32 42 43 49 192 38.4

5 5+ + + +

= =

Median: The numbers are listed in order. The middle number is 42. Mode: There is no mode since each number occurs once.



285

22. Mean: 8 10 16 16 14 12 12 13 101 12.625

8 8+ + + + + + +

= =

Median: List the numbers in order. 8, 10, 12, 12, 13, 14, 16, 16


2+

=

Mode: 12 and 16 each occur twice, so the modes are 12 and 16.

23. 4 3 3 3 2 3 3 4 4 1 43gpa 3.07

3 3 3 4 1 14⋅ + ⋅ + ⋅ + ⋅ + ⋅

= = ≈+ + + +

24. 4,583 million 4583 1 million4583 1,000,0004,583,000,000

= ×= ×=

25. 1Area (4.2 miles)(1.1 miles)20.5(4.2)(1.1) square miles2.31 square miles

=

==

26. C = 2πr = 2π ⋅ 9 = 18π miles C ≈ 18 ⋅ 3.14 = 56.52 miles

27. a. Area length width(123.8) (80)9904

= ⋅= ×=

The area is 9904 square feet.

b. 9904 × 0.02 = 198.08 Vivian needs to purchase 198.08 ounces.

28. 14.216.123.754.0

+

The total distance is 54 miles.

Cumulative Review Chapters 1−5

1. 72 in words is seventy-two.

2. 107 in words is one hundred seven.

3. 546 in words is five hundred forty-six.

4. 5026 in words is five thousand twenty-six.

5. 46713759

+

6. 3 + 7 + 9 = 19 The perimeter is 19 inches.

7. 54329

514−

Check: 51429

543+

8. R 1121

27 326827

56542827

1

−

−

−

9. To round 278,362 to the nearest thousand, observe that the digit in the hundreds place is 3. Since this digit is less than 5, we do not add 1 to the digit in the thousands place. The number 278,362 rounded to the nearest thousand is 278,000.

10. 30 = 1 ⋅ 30 30 = 2 ⋅ 15 30 = 3 ⋅ 10 30 = 5 ⋅ 6 The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.

11. 23686

1 41618 88020, 296

×

12. 236 × 86 × 0 = 0

13. a. 7

1 7 Check: 7 × 1 = 7

b. 12 ÷ 1 = 12 Check: 12 × 1 = 12

c. 6 16= Check: 1 × 6 = 6

d. 9 ÷ 9 = 1 Check: 1 × 9 = 9

e. 20 201= Check: 20 × 1 = 20



286

f. 1

18 18 Check: 1 × 18 = 18

14. 25 17 19 39 100 5

4 4+ + +

= =

The average is 25.

15. 2 ⋅ 4 − 3 ÷ 3 = 8 − 3 ÷ 3 = 8 − 1 = 7

16. 77 ÷ 11 ⋅ 7 = 7 ⋅ 7 = 49

17. 29 9 9 81= ⋅ =

18. 35 5 5 5 125= ⋅ ⋅ =

19. 43 3 3 3 3 81= ⋅ ⋅ ⋅ =

20. 310 10 10 10 1000= ⋅ ⋅ =

21. 5 35 5 5 35 25 10 2

5 5 5x yy− − ⋅ −

= = = =

22. 2 4 2 7 4 14 4 18 6

3 3 3ac+ ⋅ + +

= = = =

23. a. The opposite of 13 is −13.

b. The opposite of −2 is −(−2) = 2.

c. The opposite of 0 is 0.

24. a. The opposite of −7 is −(−7) = 7.

b. The opposite of 4 is −4.

c. The opposite of −1 is −(−1) = 1.

25. −2 + (−21) = −23

26. −7 + (−15) = −22

27. 25 6 5 36 180⋅ = ⋅ =

28. 34 2 4 8 32⋅ = ⋅ =

29. 27 (7 7) 49− = − ⋅ = −

30. 5( 2) ( 2)( 2)( 2)( 2)( 2) 32− = − − − − − = −

31. 2( 5) ( 5)( 5) 25− = − − =

32. 23 (3 3) 9− = − ⋅ = −

33. Each part represents 13

of a whole. Four parts

are shaded, or 1 whole and 1 part. 43

or 113


of a whole. Eleven parts

are shaded or 2 wholes and 3 parts. 114

or 324


of a whole. Eleven parts

are shaded or 2 wholes and 3 parts. 114

or 324


of a whole. Fourteen

parts are shaded, or 4 wholes and 2 parts. 143

or 243

37. 252 2 126

2 2 63

2 2 3 21

2 2 3 3 7

= ⋅↓ ↓⋅ ⋅

↓ ↓ ↓⋅ ⋅ ⋅

↓ ↓ ↓ ↓⋅ ⋅ ⋅ ⋅

2 2252 2 3 7= ⋅ ⋅

38. 872562

−

39. 72 36 2 3626 13 2 13

⋅− = − = −

⋅

40. 7 9 8 7 72 7 7998 8 8 8

⋅ + += = =



287

41. 16 2 8 240 5 8 5

⋅= =

⋅

10 2 5 225 5 5 5

⋅= =

⋅

The fractions are equivalent.

42. 4 0.57175 0.5569

≈

≈

Since 0.571 > 0.556, then 4 5 .7 9>

or 4 9 367 9 63⋅ = and

5 7 359 7 63⋅ =

Since 36 > 35, then 36 3563 63

> and 4 5 .7 9>

43. 2 5 2 5 103 11 3 11 33

⋅⋅ = =

⋅

44. 5 4 21 4 21 4 7 3 4 3 12 or 18 7 8 7 8 7 4 2 7 2 2

⋅ ⋅ ⋅⋅ = ⋅ = = =

⋅ ⋅ ⋅

45. 1 1 1 1 14 2 4 2 8

⋅⋅ = =

⋅

46. 2 7 37 7 37 377 5 377 1 7 1 7 1

⋅⋅ = ⋅ = = =

⋅

47. 11 54

64

4 4 64

24

z

z

z

z

= −−

=−

− ⋅ = − ⋅−

= −

48. 6 12 5 2012 20

12 12 20 128

x xx

xx

− − = −− = −

− + = − += −

49. 763.765122.001043.8900

829.6561+

50. 89.270014.3610

127.2318230.8628

+

51. 23.6 1 decimal place0.78 2 decimal places

1 88816 52018.408 1 2 3 decimal places

×

+ =


1 752026 280028.2510 1 3 4 decimal places

×

+ =


Documents

Chapter 5 5 Section 5.1 ... FIRST STATE BANK OF FARTHINGTON FARTHINGTON, IL 64422 ... 7. 167.009 in words is one hundred sixty-seven and nine thousandths