9 Measurement

Exercise Set 9-1 1. In the English system the basic units of

measurement are the inch, foot, yard, and mile. There are 12 inches in a foot, 3 feet in a yard, and 5,280 feet in a mile.

2. The basic unit of length in the metric system is the meter; the basic unit of capacity in the metric system is the liter; the basic unit of weight in the metric system is the gram.

3. The prefixes tell us how many times (or how many divided by) the basic unit the measurement is. For example, centi means 100 so a centimeter is 1 one hundredth of a meter.

4. A unit fraction in measurement is one in which the numerator and the denominator are actually the same “length,” so that the fraction is really just equal to 1.

5. In dimensional analysis unit fractions are used to convert to equivalent fractions. The units we want to keep are in the numerator and the ones we want to get rid of are in the denominator.

6. A good rule of thumb for relating inches and centimeters is that two inches is about equal to 5 centimeters.

7. 3 feet = 1 yard; multiply by 1 yard3 feet

.

12 feet 1 yard1 3 feet

×12 yards 4 yards3

= =

8. 12 inches = 1 foot; multiply by 1 foot12 inches

.

36 in. 1 ft1 12 in.

×36 ft 3 ft12

= =

9. 3 feet = 1 yard; multiply by 1 yard3 feet

.

17 ft 1 yd1 3 ft

×17 2yd 5 yd3 3

= =

10. 5,280 feet = 1 mile; multiply by 1 mile5,280 feet

.

10,345 ft 1 mi1 5,280 ft

×

10,345 mi 1.96 mi5,280

= ≈

11. 3 feet = 1 yard; multiply by 3 feet1 yard

.

113 yd4 3 ft1 1 yd

×53 159 33 =39 ft4 4 4

= × =

12. 1,760 yards = 1 mile; multiply by 1,760 yards1 mile

0.35 mi 1,760 i1yd

1 m× 0.35 1,760 yd 616 yd= × =

13. 12 inches = 1 foot; multiply by 1 foot12 inches

.

21in. 1 ft×1 12 in.

21 3ft 1 ft12 4

= =

14. 3 feet = 1 yard; multiply by 3 feet1 yard

.

147 yd2 3 ft1 1 yd

×1 95 28547 3 = 3= ft2 2 2

1142 ft2

= × ×

=

15. 36 inches = 1 yard; multiply by 1 yard .36 inches

18 in. 1 yd1 36 in.

×18 1 yd yd36 2

= =

466

16. 12 inches = 1 foot; 5,280 feet = 1 mile;

multiply by 1 foot 1 mile12 inches 5,280 feet

×

5, 237,834 in.1

1ft×

12 in.1 mi

5,280 ft×

5,237,834 mi 82.67 mi12 5,280

≈=×

17. 36 inches = 1 yard; multiply by 1 yard .36 inches

876 in. 1 yd1 36 in.

× 13

876 yd 24 yd36

= =

18. 3 feet = 1 yard; multiply by 1 yard3 feet

.

182 ft 1 yd1 3 ft

× 23

182 yd 60 yd3

= =

19. There are 2 steps from meters to centimeters. 28 m 10 8 100 800 cm× = × =

20. There is 1 step from meters to decimeters. 10.25 m 10 0.25 10 2.5 dm× = × =

21. There is 1 step from dekameters to meters. 112 dam 10 12 10 120 m× = × =

22. There is 1 step from hectometers to dekameters.

124 hm 10 24 10 240 dam× = × =

23. There is 1 step from kilometers to hectometers. 10.6 km 10 0.6 10 6 hm× = × =

24. There is 1 step from centimeters to decimeters. 130 cm 10 30 10 3 dm÷ = ÷ =

25. There is 1 step from meters to decimeters. 190 m 10 90 10 900 dm× = × =

26. There are 3 steps from millimeters to meters. 318,426 mm 10 18,426 1,000 18.426 m÷ = ÷ =

27. There are 2 steps from centimeters to meters. 2375.6 cm 10 375.6 100 3.756 m÷ = ÷ =

28. There are 3 steps from meters to kilometers. 363 m 10 63 1,000 0.063 km÷ = ÷ =

29. There are 3 steps from meters to kilometers. 3405.3 m 10 405.3 1,000 0.4053 km÷ = ÷ =

30. There is 1 step from dekameters to hectometers.

10.0034 dam 10 0.0034 10 0.00034 hm÷ = ÷ =

31. There are 5 steps from kilometers to centimeters.

50.0237 km 10 0.0237 100,000 2,370 cm× = × =

32. There are 5 steps from centimeters to kilometers.

550,000 cm 10 50,000 100,000 0.5 km÷ = ÷ =

33. There are 6 steps from kilometers to millimeters.

60.00056 km 10 0.00056 1,000,000560 mm

× = ×=

34. There are 6 steps from millimeters to kilometers.

6650,000 mm 10 650,000 1,000,0000.65 km

÷ = ÷=

35. There are 4 steps from kilometers to decimeters.

412.75 km 10 12.75 10,000 127,500 dm× = × =

36. There are 2 steps from meters to centimeters. 239.4 m 10 39.4 100 3,940 cm× = × =

37. There is 1 step from hectometers to kilometers. 18 hm 10 8 10 0.8 km÷ = ÷ =

38. There is 1 step from decimeters to centimeters. 13,256.4 dm 10 3,256.4 10 32,564 cm× = × =

39. 5 m 100 cm⋅

1m1 in.

2.54 cm⋅

5 100 in. 196.85 in.2.54⋅

= ≈

40. 14 yd 0.9144 m1 yd

⋅ 14 0.9144 m 12.80 m= ⋅ ≈

41. 16 in. 2.54 cm⋅

1in.10 mm1cm

⋅16 2.54 10 mm

1406.4 mm

⋅ ⋅=

=

467

42. 50 m 1.0936 yd1m

⋅ 50 1.0936 yd 54.68 yd= ⋅ ≈

43. 235 ft 30.48 cm⋅

1ft1 dam

1,000 cm⋅

235 30.48 dam1,000

7.16 dam

⋅=

≈

44. 563 dm 10 cm⋅

1dm1 in.

2.54 cm⋅

563 10 in.2.54

2,216.54 in.

⋅=

≈

45.

46.

47. 219 in.3

2.54 cm⋅

1in.10 mm1cm

⋅

219 2.54 10 mm3

1499.53 mm

⋅ ⋅=

=

48. 256 km 1 mi1.61km⋅

256 mi 159 mi1.61

= ≈

49.

50. 143.75 in. 2.54 cm1in.

⋅ 143.75 2.54 cm

365.13 cm

= ⋅

=

51. 56.5 ft 30.48 cm⋅

1ft1 dm

10 cm⋅

56.5 30.48 dm10

172.21 dm

⋅=

=

52. 44,000 mm 1m⋅1,000 mm

1.0936 yd1m

⋅

44,000 1.0936 yd 48.12 yd1,000⋅

= ≈

53. 2.35 km 1 mi1.61km⋅

2.35 mi 1.46 mi1.61

= ≈

54. 837 mi 1.61 km1mi

⋅ 837 1.61 km

1,347.57 km

= ⋅

≈

55. 42 dm 1m⋅10 dm

1 yd0.9144 m⋅

42 yd

4.59 yd

⋅=10 ⋅0.9144

≈

56. 254.375 cm 1 in.2.54 cm⋅

254.375 in.2.54

100.15 in.

=

≈

57. 333 in. 2.54 cm⋅

1in.1 m

100 cm⋅

333 2.54 m100

8.46 m

⋅=

≈

58. 1, 256 km 100,000 cm⋅

1km1 in.

2.54 cm⋅

1,256 100,000 in. 49,448,818.90 in.2.54⋅

= ≈

59. 25.5 yd 3 ft

1 1 yd× 25.5 3 ft 76.5 ft= × =

He sprinted 76.5 feet.

60. 94 ft 12 in.1 1 ft

× 94 12 in. 1,128 in.= × =

94 feet is 1,128 inches.

94 ft 12 in1

×.

1 ft2.54 cm

×1 in.

1 m100 cm

×

94 12 2.54 m 28.65 m100

=

× ×=

94 feet is 28.65 meters.

61. 90 ft 1 yd1 3 ft

×90 yd 30 yd3

= =

To get to second base the batter runs 2(30) = 60 yards.

90 ft 12 in1

×.

1 ft2.54 cm

×1 in.

1 m100 cm

×

90 12 2.54 m 27.432 m100

× ×= =

To get to second base the batter runs 2(27.432) = 54.864 meters.

468

62. 45 yd 3 ft

1×

1 yd12 in.1 ft

× 45(3)(12) in.

1,620 in.

=

= He threw the ball 1,620 inches.

45 yd 3 ft

1×

1 yd12 in

×.

1 ft2.54 cm

1 in.×

45(3)(12)(2.54) cm4,114.8 cm

==

He threw the ball 4,114.8 cm.

63. 1,500 yd 1 mi

1 1,760 yd×

1,500 mi 0.85 mi1,760

= ≈

The backup is about 0.85 mile.

1,500 yd 1 mi1 1,760 yd

×1.61 km

1mi×

1,500(1.61) km 1.37 km1,760

= ≈

The backup is about 1.37 km

64. 60 in. 1 ft1 12 in.

×60 ft 5 ft12

80 in.

= =

1 ft1 12 in.

× 23

80 ft 6 ft12

= =

The mattress will not fit.

65. 126 in. 1 yd1 36 in.

×126 1yd 3 yd36 2

= =

The section for her tomatoes is 123 yards long.

66. There is one step down from deci to centi, so multiply by 10. The poster board is 60 cm by 50 cm.

There are 2 steps down from deci to milli so multiply by 100. The poster board is 600 mm by 500 mm.

67. From the base unit it is three steps down to milli, so multiply by 1,000. She used 2.3(1,000) = 2,300 milligrams of citric acid.

68. There are two steps up from milli to deci, so divide by 100. 1,000 ÷ 100 = 10, so a decipede would have 10 legs.

69. 20 laps is 20 × 700 = 14,000 m. There are three steps up from the base unit to kilo, so divide by 1,000. He ran 14,000 ÷ 1000 = 14 km. There are 1.61 km per mile, so divide 14 by 1.61 to get 8.7 mi.

70. 1 km ≈ 0.6214 mi so 10 km ≈ 10(0.6214) ≈ 6.214 mi.

71. 65 mi 1.61 km1 hour 1 mi

×km65(1.61)

hourkm104.65

hour

=

≈

72. 20 in. 2.54 cm1 1in.

× 50.8 cm

24 in.

=

2.54 cm1 1in.

× 60.96 cm=

Her picture is 50.8 cm by 60.96 cm.

73. 3 3

16 16

316

62 ft 62 12 in. 744 in. 62 ft 10 in. 754 in.

754 in.

= × =

=

2.54 cm1

×1in.

1 m100 cm

×

19.16 m≈

74. 0.5 in. 2.54 cm1

×1 in.

10 mm1cm

×

12.7 mm=

75. 1.5 in. 2.54 cm1

×1 in.

10 mm1cm

× 38.1 mm

3 in.

=

2.54 cm1

×1 in.

10 mm1cm

× 76.2 mm=

The stamp measures 38.1 mm by 76.2 mm.

76. 186,283 mi1sec

5,280 ft1 mi

×3,600 seconds

×

12

1 hrft3.54 10hr

≈ ×

77. The difference is 94,400,000 − 92,900,000 = 1,500,000 miles.

1,500,000 mi 5,280 ft

1 1 mi×

97.92 10 ft= ×

469

78. ( )1 8 2 ft4

=

2 ft 12 in.1 1 ft

× 24 in.=

He cut of 24 inches.

79. 94 ft 1 m1 3.2808 ft

= 29 m

50 ft

≈

30.48 cm1 1 ft

= 1,524 cm=

They will need about three 10 m boards to cover the length and 1,524 ÷ 8 ≈ 191 boards to cover the width. So they need approximately 191(3) = 573 boards that are 10 m by 8 cm to cover the surface.

80. 20g 20 grams per serving3 servings 320 g3

=

1,000 mg1 1 g

×20,000

3

26,666 grams per serving3

=

=

81. 100(200 mg) 20,000 mg

20,000 mg

=

1 g1 1,000 mg

× 20 g=

The bottle contains 20g of active ingredient.

82. 6 in. 1 ft1 12 in.

×1 ft2

1164 164(2) 3282

182 82(2) 1642

=

÷ = =

÷ = =

They need 2(328) + 2(164) = 984 tiles to border edges, plus 4 tiles for the corners, giving us a total of 988 tiles.

83. 400 USD 1.22 CD1 1USD

× 488 CD=

His money was worth 488 Canadian dollars.

84. 10,000,000 pesos 1 USD

1 610.045 pesos×

16,392.23 USD≈

You won a little over 16 thousand dollars; you could possibly buy a new car.

85. Her change was 60 − 54.23 = 5.77 euros.

5.77 euros 6.55957 francs1 1euro

× 37.85 francs≈

She received about 37.85 francs.

86. You paid:

750 pesos 1 USD1 9.86 pesos

× $76.06

Your friend paid:

750 pesos

≈

1 USD1 14.49 pesos

× $51.76≈

You paid $76.06 − $51.76 = $24.30 more than your friend.

For exercises 87 – 104, answers can vary; these are one guy’s interpretation. The important thing is to think about the relative sizes of the different units in both systems.

87. Meters

88. Kilometers

89. Millimeters

90. Kilometers or meters, depending on where you live

91. Centimeters

92. Kilometers

93. Millimeters

94. Centimeters

95. Yards, meters

96. Miles, kilometers

97. Inches, centimeters

98. Yards, dekameters

470

99. Inches, millimeters

100. Feet, meters

101. Yards, hectometers

102. Inches, millimeters

103. Inches, centimeters

104. Yards, meters

105. 100 yd 1 m9.12s 1.0936 yd

×m10.0264s

100 m m10.28819.72 s s220 yd

≈

≈

1 m19.75 s 1.0936 yd

×m10.1858s

200 m m10.147119.71 s s

≈

≈

The first runner is most impressive; his rate in meters per second was the smallest.

106. If you divide by 1,000 the result will have no zeros. Dividing by 1,000 is moving up three steps from centi. The units would be dekameters.

107. If you multiply by 1,000 the result will have no zeros. Multiplying by 1,000 is moving down three steps from meters. The units will be millimeters.

Exercise Set 9-2 Answers may vary, depending on rounding and on the conversion factors used.

1. A square unit is a square that measures one unit by one unit. For example a square inch is a square with sides length one inch by one inch.

2. 1 yd = 3 ft, you need to square both sides of the equation (including the 1 and 3), you cannot just square the units, therefore 1 yd2 is not 3 ft2 but 9 ft2.

3. One cubic centimeter is equal to one milliliter.

4. Answers may vary.

5. Answers may vary.

6. Answers may vary.

7. 23,456 in. 2

2

1ft1 144 in.

⋅ 2 23,456= ft = 24 ft144

8. 2245,678 ft

2

1 acre1 43,560 ft

⋅245,678= acres43,560

5.6 acres≈

9. 1,642.75 acres 21 mi1 640 acres

⋅ 2

2

1,642.75= mi640

2.6 mi≈

10. 245,678,231 yd 2

2

1 mi1 3,097,600 yd

⋅

2

2

45,678,231= mi3,097,600

14.7 mi≈

11. 218.5 yd 2

2

9 ft1 1 yd

⋅ 2 2=18.5 9 ft = 166.5 ft⋅

471

12. 27 mi

2

640 acres1 1mi

⋅ = 7 640 acres

= 4,480 acres

⋅

13. 2345 yd 2

2

9 ft1 1 yd

⋅

23,105 ft=2

1 acre1 43,560 ft

⋅

0.07 acre≈

14. 277,234,587 in. 2

2

1 ft1 144 in.

⋅

277,234,587 ft=2

1 acre144 43,560 ft

⋅

12.3 acres≈

15. 2654,543 in. 2

2

1 ft1 144 in.

⋅

2654,543 ft=2

2

1 yd144 9 ft

⋅

2505 yd≈

16. 210 yd 2

2

9 ft1 1 yd

⋅290 ft=

2

2

144 in.1 1ft

⋅

2=12,960 in.

17. 252 ft 2

2

0.093 m1 1 ft

⋅ 24.84 m≈

18. 240.83 m 2

21 yd

1 0.836 m⋅ 248.8 yd≈

19. 216.6 mi 2

22.59 km

1 1 mi⋅ 243 km≈

20. 32 acres 22.59 km1 640 acres

⋅ 20.13 km≈

21. 219.3 in. 2

2

6.45 cm1 1 in.

⋅ 2124.49 cm≈

22. 218 ft 20.093 m

1⋅

21 ft

2

2

100 dm

1 m⋅

2167.4 dm≈

23. 25.666 yd 20.836 m

1⋅

21 yd

2

2100 dm

1 m⋅

2473.7 dm≈

24. 215.6 m 2

2

1 ft1 0.093 m

⋅ 2167.74 ft≈

25. 2156.875 km

2

640 acres1 2.59 km

⋅

38,764.5 acres≈

26. 280,000 cm 2

2

1 in.1 6.45 cm

⋅

212,403.10 in.≈

27. 219.4 cm 21 m

1⋅

210,000 cm

2

2

1 ft

0.093 m⋅

20.021 ft≈

28. 2256.666 in. 26.45 cm

1⋅

21 in.

2

21 dm

100 cm⋅

216.6 dm≈

29. 235 yd 2

2

0.836 m1 1 yd

⋅ 229.26 m≈

30. 152 acres 21 mi1

⋅640 acres

2

2

2.59 km

1 mi⋅

20.62 km≈

31. 21,327.5 dm 21 m

1⋅

2100 dm

2

21 ft

0.093 m⋅

2142.7 ft≈

32. 21,000,000 m 2

2

1 yd1 0.836 m

⋅

21,196,172.25 yd≈

472

33. 33 ft 7.48 gal

1⋅

31 ft

4 qt⋅1 gal

2 pt⋅1 qt

16 fluid oz1 pt

⋅

2,872.32 fluid oz≈

34. 400 gal 31 ft

1 7.48 gal⋅ 353.48 ft≈

35. 3,724 gal 31 yd

1 202 gal⋅ 318.44 yd≈

36. 12,561 oz 1 pt1

⋅16 oz

1 qt⋅2 pt

1 gal4 qt⋅

98.13 gal≈

37. 312,000 in. 3

3

1 ft1 1728 in.

⋅

36.94 ft≈

38. 322,000 ft

3

7.48 gal1 1 ft

⋅

164,560 gal≈

39. 54.375 pt 1 qt

1⋅2 pt

1 gal⋅

4 qt

3231 in.1 gal

⋅

31,570.1 in.≈

40. 34,532 in.

3

1 gal1 231 in.

⋅ 19.62 gal≈

41. 97 mL 31 cm1

⋅1 mL

3

3

1 m

1,000,000 cm⋅

30.000097 m=

42. 328.5 cm

3

1 mL1 1cm

⋅ 28.5 mL=

43. 338.251 dm 31, 000 cm

1⋅

31 dm

1 L⋅

31,000 cm

10 dL

1 L⋅

382.51 dL=

44. 433 mL 31 cm1 1 mL

⋅ 3433 cm=

45. 387,250 cm

3

1 L1 1,000 cm

⋅ 87.25 L=

46. 67.4167 L 31,000 cm1 1 L

⋅ 367,416.7 cm≈

47. 437 cL 1 L1

⋅100 cL

31,000 cm⋅

1 L

3

3

1 m

1,000,000 cm⋅

30.00437 m=

48. 1.6 L 31,000 cm1 1 L

⋅ 31,600 cm=

49. There are 3 steps from milliliters to liters. 3500 mL 10 500 1,000 0.5 L÷ = ÷ =

50. There are 2 steps from hectoliters to liters. 296.7 hL 10 96.7 100 9,670 L× = × =

51. There is 1 step from liters to deciliters. 192 L 10 92 10 920 dL× = × =

52. There is 1 step from dekaliters to hectoliters. 184.5 daL 10 84.5 10 8.45 hL÷ = ÷ =

53. There are 3 steps from liters to milliliters. 342 L 10 42 1,000 42,000 mL× = × =

54. There are 2 steps from liters to hectoliters. 292 L 10 92 100 0.92 hL÷ = ÷ =

55. 12 gal 4 qt

1⋅1 gal

1 L1.06 qt⋅ 45.28 L≈

56. 1.9 L 1.06 qt1

⋅1 L

1 gal4 qt⋅ 0.5035 gal≈

57. 378.6 qt 1 L

1⋅1.06 qt

1,000 mL1 L

⋅ 357,169.8 mL≈

58. 1,500 mL 1 L1

⋅1,000 mL

1.06 qt1 L

⋅ 1.59 qt≈

59. 21,050 mL 1 L1

⋅1,000 mL

1.06 qt1 L

⋅ 22.31 qt≈

473

60. 27.5 qt 1 L

1⋅1.06 qt

1,000 mL1 L

⋅ 25,943.4 mL≈

61. 175.2 kL 1,000 L

1⋅

1 kL1.06 qt⋅

1 L1 gal4 qt⋅

46,428 gal≈

62. 940 pt 1 qt

1⋅2 pt

1 L⋅1.06 qt

1 kL1,000 L⋅

0.44 kL≈

63. 11,460 oz 1 pt1

⋅16 oz

1 qt⋅2 pt

1 L⋅1.06 qt

1 kL1,000 L⋅

0.34 kL≈

64. 84.1 kL 1,000 L1

⋅1 kL

1.06 qt⋅

1 L1 gal4 qt⋅

22,286.5 gal≈

65. 3733.5 ft

362.5 lb

1 1 ft⋅ 45,843.75 lb≈

66. 323 ft

3

64 lb1 1 ft

⋅ 1,472 lb≈

67. 205.75 lb 31 ft1 62.5 lb

⋅ 33.3 ft≈

68. 742.4 lb 31 ft1 64 lb

⋅ 311.6 ft≈

69. 269,120 in. 2

2

1 ft1 144 in.

⋅ 2480 ft=

Since a gallon only covers 400 ft2 she should buy 2 gallons (unless, of course, the paint comes in smaller size containers).

70. 215 m 2

2

1 ft1 0.093 m

⋅ 2

2

2

161.3 ft

161.3 ft 8.06520 ft

≈

=

Jose will need approximately 8 bags of mulch, which will cost him $2(8) = $16.

71. 3200 ft 3

3

1 yd1 27 ft

⋅ 37.4 yd≈

Dan should ask for about 7.4 cubic yards.

72. 40 oz 1 pt1 16 oz

⋅ 2.5 pt=

Chloe drank 2.5 pints of soda, therefore she filled the pint glass 2.5 times.

73. 1,000 acres 21 mi1 640 acres

⋅ 21.56 mi≈

The campus covers about 1.56 mi2.

74. 5 acres 243,560 ft1

⋅1acre

2

2

1 yd9 ft⋅ 224,200 yd=

The extension covers 24,200 yd2.

75. 5 gal 31 ft

1 7.48 gal⋅ 30.67 ft≈

Approximately 0.67 ft3of water was added.

76. 3(0.5)(0.25) m 3 3

3

100 cm1 1 m

⋅ 325,000 cm=1

There are 125,000 ÷ 100 = 1,250 doses of the drug left.

77. 232 ft 2

2

144 in.1 1 ft

⋅ 24,608 in.=

Since each tile covers 8 in2 she will need 4,608 ÷ 8 = 576 tiles. To allow for 10%

breakage, she will need 576 1.10 634× ≈ tiles.

78. 122 qt 1 gal

1⋅

4 qt30.5 gal=

The store can fill about 30 gallon containers. To allow for 5% spillage, the store can fill, 30.5 0.95 28× ≈ gallon containers.

79. 35 ft

3

64 lb1 1 ft

⋅ 320 lb≈

The water weighs 320 lb, the boat weighs 200 lb for a total weight of 520 lb.

474

80. 210,000 in. 21 ft

1⋅

2144 in.

2

2

1 yd9 ft⋅ 27.72 yd≈

She should get about 7¾ square yards of fabric. To allow for cutting waste, she should allow for 7.75 1.10 8.5× ≈ yards.

81. 8(20) oz 1 pt1

⋅16 oz

1 qt2 pt⋅ 5 qt=

She has enough Gatorade for 5 bikers.

82. 1,500 gal 31 yd

1 202 gal⋅ 37.43 yd≈

There is enough dirt for 7.43 ÷ 2 ≈ 3.7 planters.

83. 26 mi 2

2

2.59 km1 1 mi

⋅ 215.54 km≈

The search party covered about 15½ km2.

84. 200 gal 31 ft

1⋅7.48 gal 3

62.5 lb

1 ft⋅ 1,671 lb≈

165 kg 2.2 lb

1⋅

1kg363 lb≈

The water weighs about 1,671 lb. The tub

weighs 50 pounds and the two people together weight about 363 pounds. The total weight is 1,671 + 50 + 363 = 2,084 lb.

85. Acres

86. Square feet

87. Square miles

88. Square feet

89. Square miles

90. Square feet

91. Liters

92. Kiloliters

93. Milliliters

94. Kiloliters

95. 310 yd 3

3 3

1 m1 (1.0936) yd

⋅ 37.65 m≈

The capacity of one dump truck is about 7.65 cubic meters. Since there are three trucks one trip will haul away 3 × 7.65 = 22.95 m3 of dirt. It will take 200 ÷ 22.95 ≈ 9 trips to remove all the dirt.

96. 3200 m 3 3(1.0936) yd

1⋅

31 m 3

202 gal

1 yd⋅

52,839 gal≈

There are 52,839 gallons of water in the hole. The two pumps can pump

2(750) = 1,500 gallons per minute. It will take 52,839 ÷ 1,500 = 35 minutes to pump all the water out of the hole.

97. Answers may vary.

98. $1.27 $1.27

L L=

1 L⋅

$4.79

0.265 gal gal=

$3.89 per gallon is the better price.

99. Answers may vary. depending on your school.

100.

a)

600,000 gal

1 sec

3, 600 sec⋅

31 ft

1 hr⋅

7.48 gal

62.5 lb

31 ft

1 ton

2000 lb⋅

9, 024, 000 ton

hr≈

b) 600,000 gal 31 ft

1 sec 7.48 gal⋅

380,214 ftsec

≈

The Rogers Centre is 56.5 million cubic feet, so it would take:

3

356,500,000 ft 1 sec 704 sec

1 80,214 ft⋅ ≈

704 seconds = 11 minutes and 44 seconds 101. Answers may vary, depending on your

classroom.

475

102. a) Answers may vary, depending on your classroom.

b) Answers may vary, depending on your classroom.

c) The building is 129,428,000 cubic feet, so it would hold:

3129,428,000 ft3

7.48 gal1 1 ft

⋅ 968,121,440 gal≈

And the water would weigh:

3129,428,000 ft 62.5 lb1

⋅31 ft

1 T2000 lb

4,044,625 T

⋅

=

103. a)

16 ounce 1 qt1

⋅32 ounce

1 L⋅1.06 qt

1000 mL⋅

1 L20 drops1 mL

⋅

9,434 drops≈

b)

1,000,000 drops 1 mL1

⋅20 drops

1 L⋅1000 mL

1.06 qt⋅

1 L

1 gal

⋅

4 qt

3 1 ft⋅7.48 gal 3

62.5 lb1 ft

⋅

110.7 lb≈

c)

82,500,000 mL 20 drop1

⋅1 mL

1 sec⋅1 drop

1 day⋅86,400 sec

19,097 days≈ 19,097 days is equal to 52 years and 117 days.

104.

a)

20 gal 128 ounce

1⋅

1 gal

1 t⋅

0.16 ounce

5 sec⋅

1 t

1 min

60 sec⋅

1, 280 min≈

1,280 minutes is equal to 21 hours and 20 minutes.

b)

382.5 m 1 kL1

⋅31 m

1,000 L⋅

1 kL1.06 qt⋅

1 L32 ounce⋅

1 qt

1 t

⋅

0.16 ounce5 sec⋅

1 t1 day

86,400 sec⋅

971 days≈ 971 days is equal to 2 years and 241 days.

c)

31.25 mi 11 31.48 10 ft×⋅

31 mi

7.48 gal⋅

31 ft128 ounce

1 gal⋅

1 t

⋅

0.16 ounce5 sec⋅

1 t1 day

86,400 sec⋅

1 year365 day

168,500,000 years

⋅

≈ d)

377,640,000 mi 11 31.48 10 ft1

×⋅

31 mi

7.48 gal⋅

31 ft128 ounce

1 gal⋅

1 t

⋅

0.16 ounce5 sec⋅

1 t1 day

86,400 sec⋅

16

1 year365 day

1.05 10 years

⋅

≈ × Can you imagine how frustrating it would be if

it started raining while you were working on b, c, or d?!

Exercise Set 9-3 1. Mass is a measure of the amount of matter in

an object and weight is a measure of the amount of force acting on that object.

2. On earth we can treat weight and mass the same because the gravitational force on a body is the same.

3. A gram is not very much matter at all. We need to use kilograms so that we don’t have to write down the weights of things using large numbers.

4. In most metric measures, there are different units. For example, milligrams, grams, and kilograms which all measure the same thing – mass. But in temperature, there is only one unit and that unit is degrees Celsius.

5. Water freezes at 0 degrees and boils at 100 degrees, both of which are powers of ten.

6. It is an extension of the Celsius scale where zero represents absolute zero instead of the temperature at which water freezes.

7.

33 oz 1 lb1 16 oz

⋅ 2.0625 lb=

476

8. 92.6 oz 1 lb1 16 oz

⋅ 5.7875 lb=

9. 2.3 1b 16 oz1 1 lb

⋅ 36.8 oz=

10. 3.3125 1b 16 oz1 1 lb

⋅ 53 oz=

11. 4.2 T 2,000 lb1 1 T

⋅ 8,400 lb=

12. 7.45 T 2,000 lb1 1 T

⋅ 14,900 lb=

13. 3,500 lb 1 T1 2,000 lb

⋅ 1.75 T=

14. 2,350 lb 1 T1 2,000 lb

⋅ 1.175 T=

15. 34,567 oz 1 lb1

⋅16 oz

1 T2,000 lb⋅ 1.08 T≈

16. 5.875 T 2,000 lb1

⋅1 T

16 oz1 lb⋅ 188,000 oz=

17. There is 1 step from decigrams to centigrams. 19 dg 10 9 10 90 cg× = × =

18. There is 1 step from milligrams to centigrams. 16 mg 10 6 10 0.6 cg÷ = ÷ =

19. There is 1 step from kilograms to hectograms. 144 kg 10 44 10 440 hg× = × =

20. There are 2 steps from hectograms to grams. 216.34 hg 10 16.34 100 1,634 g× = × =

21. There is 1 step from centigrams to decigrams. 151.5 cg 10 51.5 10 5.15 dg÷ = ÷ =

22. There is 1 step from grams to dekagrams. 1181.6 g 10 181.6 10 18.16 dag÷ = ÷ =

23. There is 1 step from grams to decagrams. 17.26 g 10 7.26 10 72.6 dg× = × =

24. There are 3 steps from grams to milligrams. 30.325 g 10 0.325 1,000 325 mg× = × =

25. There are 2 steps from centigrams to grams. 23,217 cg 10 3,217 100 32.17 g÷ = ÷ =

26. There are 2 steps from dekagrams to kilograms.

219.25 dag 10 19.25 100 0.1925 kg÷ = ÷ =

27. There are 3 steps from milligrams to grams. 35.43 mg 10 5.43 1,000 0.00543 g÷ = ÷ =

28. There are 3 steps from grams to kilograms. 3400 g 10 400 1,000 0.4 kg÷ = ÷ =

29. There are 3 steps from kilograms to grams. 322.5 kg 10 22.5 1,000 22,555.6 g× = × =

30. There are 2 steps from grams to hectograms. 25,632 g 10 5,632 100 56.32 hg÷ = ÷ =

31. 120 g 1 oz

1 28 g⋅ 4.29 oz≈

32. 15.75 oz 28 g1 1 oz

⋅ 441 g≈

33. 4,823 cg 1 kg

1⋅100,000 cg

2.2 lb1 kg⋅

0.106 lb≈

34. 27 t 1,000 kg1

⋅1 t

2.2 lb1 kg⋅ 59,400 lb≈

35. 3 T 2,000 lb1

⋅1 kg

1 T⋅2.2 lb

10 hg1 kg⋅

27,272.73 hg≈

36. 14 dg 1 g

1⋅10 dg

1 oz28 g⋅ 0.05 oz≈

37. 357,201 lb 1 kg1

⋅2.2 lb

1 t1,000 kg⋅

162.36 t≈

477

38. 13 lb 1 kg1

⋅2.2 lb

10,000 dg1 kg

⋅ dg≈ 59,090.91

39. 5.75 T 2,000 lb1

⋅1 T

1 kg⋅2.2 lb

1 t1,000 kg⋅

5.23 t≈

40. 16.3 t 1,000 kg1

⋅1 t

2.2 lb⋅

1 kg1 T

2,000 lb⋅

17.93 T≈

41. 213 oz 28 g1

⋅1 oz

10 dg1 g

⋅ 59,640 dg≈

42. 64 lb 1 kg1

⋅2.2 lb

100 dag1 kg

⋅ 2,909.09 dag≈

43. 815 dag 10 g

1⋅1 dag

1 oz28 g⋅ 291.07 oz=

44. 550 hg 100 g

1⋅

1 hg1 oz28 g⋅ 1,964.29 oz≈

45. 14,625 mg 1 kg

1⋅1,000,000 mg

2.2 lb1 kg⋅

0.03 lb≈

46. 41 lb 1 kg1

⋅2.2 lb

1,000 g1 kg

⋅ 18,636.36 g≈

47. 9 932 (14) 32 57.2 F5 5

F C= + = + = °

48. 9 932 (27) 32 80.6 F5 5

F C= + = + = °

49. 9 9 132 (33 ) 32 92 F5 5 3

F C= + = + = °

50. 9 932 ( 5) 32 23 F5 5

F C= + = − + = °

51. 9 932 ( 18) 32 0.4 F5 5

F C= + = − + = − °

52. 9 9 132 ( 30 ) 32 22.9 F5 5 2

F C= + = − + = − °

53. 5 5( 32) (5 32) 15 C9 9

C F= − = − = − °

54. 5 5( 32) (27 32) 2.78 C9 9

C F= − = − ≈ − °

55. 5 5( 32) (96.2 32) 35.7 C9 9

C F= − = − ≈ °

56. 5 5( 32) ( 3 32) 19.44 C9 9

C F= − = − − ≈ − °

57. 5 5( 32) ( 10 32) 23.33 C9 9

C F= − = − − ≈ − °

58. 5 5( 32) ( 5.25 32) 20.7 C9 9

C F= − = − − ≈ − °

59. 273.15 219.3 273.15 53.85CC K= − = − = −

60. 273.15 5 273.15 278.15CC K= − = − − = −

61. 273.15 251 273.15 22.15CC K= − = − = −

9 932 ( 22.15) 32 7.9 F5 5

F C= + = − + ≈ − °

62. 273.15 256 273.15 529.15CC K= − = − − = −

9 932 ( 529.15) 32 920.5 F5 5

F C= + = − + ≈ − °

63. 273.15 100.32 273.15 172.83CC K= − = − = −

9 932 ( 172.83) 32 279.1 F5 5

F C= + = − + ≈ − °

64. 273.15 462.25 273.15 189.1CC K= − = − =

9 932 (189.1) 32 372.4 F5 5

F C= + = + ≈ °

65. 100 oz 1 lb1 16 oz

⋅ 6.25 lb=

The parents are not correct; a 6.25 lb baby is average.

66. 1,700 lb 1 T1 2,000 lb

⋅ 0.85 T=

The load is more than ¾ ton. Billy’s truck will not be able to handle the load.

67. 4,400 kg 2.2 lb

1 1 kg⋅ 9,680 lb≈

478

The elevator is capable of holding 9,680 lb. The men weigh a total of about

210 × 10 = 2,100 lb. The elevator is more than able to hold their weight.

68. 68 kg 2.2 lb

1 1 kg⋅ 149.6 lb≈

Susan’s weight is above the healthy weight for her height; her doctor might suggest she go on a diet.

69. 9 932 (35) 32 95 F5 5

F C= + = + = °

That’s pretty hot! It’s a bathing suit and flip-flops for Olivia.

70. 24 oz 1 lb1 16 oz

⋅ 1.5 lb=

Janine needed to buy 1.5 pounds of chicken.

71. 5(2,540) lb 1 T1 2,000 lb

⋅ 6.35 T=

The cars weigh more than the capacity of the

ferry; better get your life vests!

72. 750 g 1 oz

1 28 g⋅ 26.8 oz=

26.8 8.933

≈

He can completely fill 8 jars and almost fill 9.

73. 9 932 (20) 32 68 F5 5

F C= + = + = °

It is 68°F.

74. 9 932 (38.8) 32 101.84 F5 5

F C= + = + = °

You appear to have a fever.

75. 5 lb 16 oz1

⋅1 lb

28 g1 oz⋅ 2,240 g≈

They seized 2,240 grams of the substance.

76. 3,000 kg 1 t

1 1,000 kg⋅ 3 t=

The truck poured too much sand into the foundation.

77. 3.6 lb 16 oz1 1 lb

⋅ 57.6 oz=

She lost 57.6 oz of fat.

78. 4(12) + 2(20) = 88 oz

88 oz 1 lb1 16 oz

⋅ 5.5 lb=

They ate 5.5 lb of steak.

79.

If they let the man on, the total weight on the elevator will be 2,260 pounds which exceeds the weight limit. They should not let him on!

80. 9 932 (2,000) 32 3,632 F

5 5F C= + = + = °

Her heating element will not be hot enough.

81. 9 9 3(7) 12 F5 5 5

F C= = = °

The temperature will go down by 312 F5° 44.

82. ( )5 5 2( ) 22 12 C9 9 9

C F= = ≈ °

The temperature went up by 212 C9° .

83. 25 kg

32.2 lb1 kg1 ft⋅ 3

lb55ft

≈

Yuan did not buy the right cement.

84. 1.7 T 2,000 lb1

⋅1 T

1 kg2.2 lb⋅

1,545.5 kg≈

The scale reads approximately 1,545.5 kg

1,000 kg 2.2 lb1 1 kg

⋅ 2,200 lb≈

479

85. 5 5( 32) (222.8 32) 106 C9 9

C F= − = − = °

The sugar should be melted.

86. 15 kg 1,000,000 mg

1 1 kg⋅

200,000 mg=

There are 200,000 mg of the substance. To fill 50 bags with 4,500 mg each would require 50(4,500) = 225,000 mg. There is not enough to fill 50 bags.

87. 450 lb 1 kg1 2.2 lb

⋅ 204.5 kg≈

The person would have to weigh 204.5 – 137 = 67.5 kg.

88. No. Answers may vary.

89. a)

C 9 325

F C= +

14 57 17 63 21 70 26 79 31 88 38 100 41 106 39 102 35 95 28 82 19 66 14 57

The Celsius graph appears to show a greater

variation in temperatures.

b)

0

20

40

60

80

100

120

1 2 3 4 5 6 7 8 9 10 11 12

Avg.

Hig

h (°

F)

Month

50

60

70

80

90

100

110

1 2 3 4 5 6 7 8 9 10 11 12

Avg.

Hig

h (°

F)

Month

480

90. a)

Millions of pounds

Metric Tons

19.7 8,955 20.1 9,136 17.8 8,091 19.6 8,909 23.3 10,591 24.7 11,227 19.7 8,955 22.3 10,136 21.9 9,955 20.7 9,409 15.3 6,955

b) The variation appears to be much greater in the original graph. This is largely due to the fact that the vertical axis is scaled differently: the lowest height on the graph is 14 million pounds, not zero pounds.

91. San Antonio

92. Louisville

93. Football player

94. Kid

95. Kilogram

96. Metric Ton

97. Gram

98. Kilogram

Review Exercises

1.

14 yd2 3 ft

1 1 yd⋅

113 ft2

=

2. 23,564 ft 1 mi1 5,280 ft

⋅ 4.46 mi≈

3. 21 in. 1 ft1 12 in.

⋅ 1.75 ft=

4. 356 in. 1 ft1

⋅12 in.

1 yd3 ft⋅ 9.89 yd≈

5. 8, 245,264 in. 1 ft1

⋅12 in.

1 mi5,280 ft⋅ 130.13 mi≈

6. There are 2 steps down from meters to centimeters.

210.2 m 10 1,020 cm⋅ =

7. There is 1 step down from meters to decimeters.

0.36 m 10 3.6 dm⋅ =

8. There are 4 steps down from kilometers to decimeters.

413.54 km 10 135,400 dm⋅ =

0

2

4

6

8

10

12

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

Thou

snad

s of M

etric

Ton

s

Year

481

9. There are 3 steps up from millimeters to meters.

334,500 mm 10 34.5 m÷ = 10. There is 1 step up from dekameters to

hectometers. 0.56 dam 10 0.056 hm÷ =

11. 7.375 m 3.2808 ft

1⋅

1m12 in.1ft

⋅ 290.35 in.≈

12. 35.21m 1.0936 yd

1 1m⋅ 38.51 yd≈

13. 85 cm 1 in.1 2.54 cm

⋅ 33.46 in.≈

14. 23.3 yd 0.9144 m

1⋅

1 yd10 dm1m

⋅ 213.36 dm≈

15. 345 ft 0.3048 m1

⋅1ft

10 dm1m

⋅ 1,051.56 dm=

16.

17. 100 yd 0.9144 m

1 1 yd⋅ 91.44 m=

18. 10 km 1 mi1 1.61km

⋅ 6.21 mi≈

19. 205 mi 1.61 km1 hr 1 mi

⋅ kmhr330 ≈

205 mi

1 hr1 hr

⋅60 min

1 min⋅

5,280 ft60 sec 1 mi

⋅

ftsec300.67 ≈

20. 3,600 m 1 km1

⋅1,000 m

1 mi1.61km⋅ 2.24 mi≈

It would take mi

hr

2.24 mi 0.75 hr3

≈ to walk the

distance at 3 miles per hour, or about 45 minutes.

21. 1,986 ft 1 m1

⋅3.2808 ft

605.34 m≈

The Eiffel Tower is about 605 m tall, which is

taller than the Chrysler building in New York City.

22. Kilometers

23. 25,698 in. 2

2

1ft1 144 in.

⋅ 239.57 ft≈

24. 2543 yd 29 ft

1⋅

21 yd 2

1 acre43,560 ft⋅ 0.11 acre≈

25. 22.45 mi 2

2

27,878,400 ft1 1mi

⋅ 268,302,080 ft=

26. 2456,321in. 2

2

1 yd1 1,296 in.

⋅ 2352.10 yd≈

27. 5,643 acres 21 mi1 640 acres

⋅ 28.82 mi≈

28.

223.1 in. 2

26.45 cm

1 1 in.⋅ 2149.1 cm≈

29. 214.1 ft 20.093 m

1⋅

21 ft

2

2100 dm

1 m⋅ 2131.13 dm≈

30. 123.5 acres 24,047 m1

⋅1acres

2

2

1 km1,000,000 m⋅

20.50 km≈

31. 232.5 cm 21in.

1⋅

26.45 cm

2

2

1 ft144 in.⋅ 20.03 ft≈

32. 2324 km 21,000,000 m

1⋅

21km

2

2

1 ft0.093 m⋅

23, 483,870,968 ft≈

33. 37 ft 7.48 gal

1⋅

31ft

4 qt⋅1gal

2 pt⋅

1qt16 oz1pt

⋅

6,702 oz≈

482

34. 342,000 ft 3

3

1,728 in.1 1ft

⋅ 372,576,000 in.=

35. 36 yd

3

202 gal1 1 yd

⋅ 1,212 gal≈

36. 3.5 L 1,000 mL1

⋅1 L

31 cm1 mL⋅ 33,500 cm=

37. 45 pt 1 qt

1⋅2 pt

1 gal⋅

4 qt

31 ft⋅7.48 gal

3

3

1,728 in.

1 ft⋅

31,299.47 in.≈

38. 312 L 1,000 mL

1 1 L⋅ 312,000 mL=

39. 673 hL 100 L1 1 hL

⋅ 67,300 L=

40. 54,457 mL 1 kL1 1,000,000 mL

⋅ 0.054457 kL=

41. 231 cL 1 L1 100 cL

⋅ 2.31 L=

42. Since 1 cc = 1 mL the patient is in danger.

43. 32.27 ft

3

7.48 gal1 1 ft

⋅ 17 gal≈

He should use 17(5) = 85 drops.

44.

45. 2 acre 243,560 ft1 1acre

⋅ 287,120 ft=

Price per ft2 of each:

2

$41,00087,120 ft

2

2

2

$0.47 per ft

$46,000 0.093 m9,500 m

≈

⋅ 22 $0.45 per ft

1 ft≈

The second property is cheaper per square

foot.

46.

They should charge $483.87 for a 5,000 square

meter lawn.

47. Acres

48. Cubic centimeters

49. 65 oz 1 lb1 16 oz

⋅ 4.0625 lb=

50. 2.4 T 2,000 lb1 1 T

⋅ 4,800 lb=

51. 34,500 lb 1 T1 2,000 lb

⋅ 17.25 T=

52. 1.3 T 2,000 lb1

⋅1 T

16 oz1 lb⋅ 41,600 oz=

53. 567,376 oz 1 lb1

⋅16 oz

1 T2,000 lb⋅ 18 T≈

54. There is 1 step down from decigrams to centigrams.

9.75 dg (10) 97.5 cg⋅ =

55. There are 3 steps down from grams to milligrams.

0.457 g (1,000) 457 mg⋅ =

56. There are 3 steps down from kilograms to grams.

5.6 kg (1,000) 5,600 g⋅ =

57. There are 2 steps up from grams to hectograms.

34,345 g (100) 343.45 hg÷ =

58.

59.

483

60. 192.125 oz 28 g

1⋅1 oz

10 dg1 g

⋅

53,795 dg≈

61. 23,456 mg 1 g

1⋅1,000 mg

2.2 lb1,000 g⋅ 0.05 lb≈

62. 456.6 hg 1 oz

1⋅28 g

100 g⋅

1 hg1,630.7 oz⋅ ≈

63. 9 932 (13) 32 55.4 F5 5

F C= + = + = °

64. 9 9 132 ( 2.5) 32 27 F5 5 2

F C= + = − + = °

65. 5 5( 32) (92.3 32) 33.5 C9 9

C F= − = − ≈ °

66. 5 5( 32) ( 21 32) 29.44 C9 9

C F= − = − − ≈ − °

67. 273.15 241.7 273.15 31.45CC K= − = − = −

68. 273.15 8.2 273.15 264.95KK C= + = − + =

69. 3,200 g 2.2 lb

1⋅1,000 g

7.04 lb≈

70. 9 932 (38.5) 32 101.3 F5 5

F C= + = + = °

Heinrich has a fever.

71. 8° Celsius higher is the same as: 9 9 (8) 14.4 F5 5

F C= = = °

So, the high temperature was about 52˚F + 14.4˚F = 66.4˚F.

72. Amount lost:

58 kg 2.2 lb

1 1kg⋅ 127.6 lb

346 lb 127.6 lb 218.4 lb

≈

− =

His ending weight was about 218.4 lb.

73. 1 T 2,000 lb

1⋅

1 T1 kg

⋅2.2 lb

1 t1,000 kg⋅

0.909 t≈

The cost on the American side is $65 for 0.909 t and on the Canadian side it is $58 for 1 t. It appears the deal on the Canadian side is better, but only if they’re both using the same currency!

Chapter Test

1. 132 in. 1 yd1 36 in.

⋅ 3.67 yd≈

2. 8,665 ft 1 mi1 5,280 ft

× 1.64 mi≈

3. There are 2 steps down from meters to

centimeters. 0.123 m 100 = 12.3 cm⋅

4. There are 3 steps down from hectometers to decimeters.

2 hm 1,000 = 2,000 dm⋅

5. 34 cm 1 in.1 2.54 cm

⋅ 13.39 in.≈

6. 27.5 ft 0.3048 m

1 1 ft⋅ m≈ 8.382

7. 23,475 in. 2

2

1ft1 144 in.

⋅ 224.13 ft≈

8. 3, 235 acres 21 mi1 640 acres

⋅ 25.05 mi≈

484

9. 221.32 cm 2

2

1 in.1 6.45 cm

⋅ 23.31 in.≈

10. 219.3 ft 2

2

0.093 m1 1ft

⋅ 21.80 m≈

11. 3100 cm 3

3 3

1 in.1 2.54 cm

⋅ 36.10 in.≈

12. 315,154 in. 3 3 2.54 cm

1⋅

31 in.

3

3 3

1 m 100 cm⋅

30.25 m≈

13. 34.19 yd

3

202 gal1 1 yd

⋅ 846.38 gal≈

14. 34.25 pt 1 qt

1⋅2 pt

1 gal⋅

4 qt

3231 in.1 gal

⋅ 3988.97 in.≈

15. 365 oz 1 lb1 16 oz

⋅ 22.8125 lb=

16. 34,675 oz 1 lb1

⋅16 oz

1 T2,000 lb⋅ 1.08 T≈

17. There is 1 step down from decigrams to

centigrams. 5.91 dg 10 = 59.1 cg⋅

18.

19. 2,854 cg 1 g

1⋅100 cg

2.2 lb1,000 g⋅ 0.06 lb≈

20. 9 932 (13) 32 55.4 F5 5

F C= + = + = °

21. 5 5( 32) (85.2 32) 29.56 C9 9

C F= − = − ≈ °

22. 26 mi 1.61 km

1 1 mi⋅ 41.86 km≈

385 yd 0.9144 m

1⋅

1 yd1 km

1000 m⋅ 0.35 km≈

41.86 km + 0.35.km ≈ 42.2 km

23. 26 mi 5,280 ft

1 1 mi⋅ 137,280 km≈

385 yd 3 ft

1 1 yd⋅ 1,155 km≈

The total number of feet is 137,280 + 1,155 = 138,435 feet.

138,435 ft 1 sec

1 ⋅5.9 ft

1 min60 sec⋅ 391 min≈

391 min = 6 hours and 31 minutes

24. 88 kg 2.2 lb

1 1kg⋅ 194 lb

194 180 14 lb

≈

− =

Bobby is 14 pounds overweight.

25. 2 2

22

1 yd 9 ft$12.50 $1.39 per ft9 ft

=

≈

The first at $1.39 per square foot is cheaper than the second at $1.70 per square foot.

26. 5 km 1,000 m1

⋅1 km

3.2808 ft1 m

⋅ 16,404 ft≈

27. 353 km 1 mi1 1.61 km

⋅ 219.25 mi≈

It will take approximately 219.25 ÷ 65 ≈ 3.37 hours.

28. 2.4 112 26.2 140.6 miles140.6 mi

+ + =1.61 km

1 1 mi⋅ 226.366 km≈

Yes, the total distance covered is approximately 26.4 km more than a 200 km car race.

29. 23,500 ft 21 yd

1 ⋅

29 ft 21 hr

20 yd⋅ 19.44 hr≈

485

30. 27, 238 ft 2

2

1 yd1 9 ft

⋅ 2804.22 yd ≈

The cost will be $40(804.22) = $32,168.80

31. 230,000 ft

2

1 acre1 43,560 ft

⋅ 0.69 acre≈

The agent is wasting her time.

32. 46,000 T 2,000 lb1

⋅1 T

1 kg2.2 lb⋅

41,818,182 kg≈

33. 9 932 (32.8) 32 91.04 F5 59 932 (24.4) 32 75.92 F5 5

The difference is 91.04 75.92 15.12 F

F C

F C

= + = + = °

= + = + = °

− = °

486