SECTION 8.4
Exercise Set 8.4
1. Dimensional analysis is a procedure used to convert from one unit of measurement to a different
unit of measurement.
2. A unit fraction is a fraction in which the numerator and denominator contain different units and the
value of the fraction is 1.
3.
60 seconds
1 minute
or
because 60 seconds = 1 minute
1 minute
60 seconds
4.
3 ft
1 yd
or
because 3 ft = 1 yd
1 yd
3 ft
5.
6.
1 ft
Since we need to eliminate centimeters, cm must appear in the denominator. Since we
30 cm
need to convert to feet, ft must appear in the numerator.
1 lb
Since we need to eliminate kilograms, kg must appear in the denominator. Since we
0.45 kg
need to convert to pounds, lb must appear in the numerator.
7.
3.8 l
Since we need to eliminate gallons, gal must appear in the denominator. Since we
1 gal
need to convert to liters, l must appear in the numerator.
8.
0.8 m 2
Since we need to eliminate square yards, yd 2 must appear in the denominator. Since we
2
1 yd
need to convert to square meters, m 2 must appear in the numerator.
 2.54 cm 
9. 52 in. = ( 52 in.) 
 = 132.08 cm
 1 in. 
 0.45 kg 
10. 9 lb = ( 9 lb ) 
 = 4.05 kg
 1 lb 
 30 cm  1 m 
11. 4.2 ft = ( 4.2 ft ) 

 = 1.26 m
 1 ft  100 cm 
 1 oz 
12. 427 g = ( 427 g ) 
 = 15.25 oz
 28 g 
 0.8 m 2 
= 12 m 2
13. 15 yd 2 = (15 yd 2 ) 
2 
 1 yd 
 1 lb 
14. 160 kg = (160 kg ) 
 = 355.5 ≈ 355.6 lb
 0.45 kg 
 1.6 km 
15. 39 mi = ( 39 mi ) 
 = 62.4 km
 1 mi 
 1 cm   1 in. 
16. 765 mm = ( 765 mm ) 

 = 30.11811024 ≈ 30.12 in.
 10 mm   2.54 cm 
 1 acre 
17. 675 ha = ( 675 ha ) 
 = 1687.5 acres
 0.4 ha 
 28 g 
18. 192 oz = (192 oz ) 
 = 5376 g
 1 oz 
285
286 CHAPTER 8 The Metric System
 1 pt 
19. 15.6 l = (15.6 l ) 
 = 33.19148936 ≈ 33.19 pints
 0.47 l 
 0.9 t 
20. 4 T = ( 4 T ) 
 = 3.6 t
 1T 
 1 fl oz 
21. 45.6 ml = ( 45.6 ml ) 
 = 1.52 fl oz
 30 ml 
 1 mi 2
22. 1.6 km 2 = (1.6 km 2 ) 
2
 2.6 km

2
 = 0.615384615 ≈ 0.62 mi

 0.45 kg 
23. 120 lb = (120 lb ) 
 = 54 kg
 1 lb 
 0.4 ha 
24. 6.2 acres = ( 6.2 acres ) 
 = 2.48 ha
 1 acre 
25. 28 grams
26. 28 grams, 0.45 kilogram
27. 0.45 kilogram
 12 in.   2.54 cm 
28. 5 ft = ( 5 ft ) 

 = 152.4 cm
 1 ft   1 in. 
 2.54 cm 
2 in. = ( 2 in.) 
 = 5.08 cm
 1 in. 
152.4 cm + 5.08 cm = 157.48 centimeters
 1m 
157.48 cm = (157.48 cm ) 
 = 1.5748 ≈ 1.57 meters
 100 cm 
29. 2.54 centimeters, 1.6 kilometers
30. 1.6 kilometers
 0.9 m 
31. 10 yd = (10 yd ) 
 = 9 meters
 1 yd 
32. 0.9 meter
 1 yd 
33. 505 m = ( 505 m ) 
 = 561. 1 ≈ 561.11 yd
 0.9 m 
 1 yd 
34. 175 m = (175 m ) 
 = 194.4 ≈ 194.44 yd
 0.9 m 
 100 cm  1 ft 
35. 344 m = ( 344 m ) 

 = 1146.6 ≈ 1146.67 ft
 1 m  30 cm 
 100 cm   1 ft 
36. 303 m = ( 303 m ) 

 = 1010 ft
 1 m   30 cm 
 1 mi 
37. 85 km = ( 85 km ) 
 = 53.125 ≈ 53.13 mph
 1.6 km 
 1.6 km 
38. 105 mi = (105 mi ) 
 = 168 km
 1 mi 
39.
( 6 yd )( 9 yd ) = 54 yd 2
 0.8 m 2 
54 yd 2 = ( 54 yd 2 ) 
= 43.2 m 2
2 
 1 yd 
SECTION 8.4
 1.6 km 
40. 110 mi = (110 mi ) 
 = 176 km
 1 mi 
 1 oz 
41. 400 g = ( 400 g ) 
 = 14.28571429 ≈ 14.29 oz
 28 g 
 1 mi 
42. 80 km = ( 80 km ) 
 = 50 mph
 1.6 km 
 30 ml 
43. 8 fl oz = ( 8 fl oz ) 
 = 240 ml
 1 fl oz 
 3.8 l   1 kl 
44. 12,500 gal = (12,500 gal ) 

 = 47.5 kl
 1 gal   1000 l 
45.
( 50 ft )( 30 ft )(8 ft ) = 12, 000 ft 3
 0.03 m3 
3
12, 000 ft 3 = (12,000 ft 3 ) 
 = 360 m
3
1
ft


 2.6 km 2 
2
46. 1189 mi 2 = (1189 mi 2 ) 
 = 3091.4 km
2
 1 mi 
 1 lb 
47. 1 kg = (1 kg ) 
 = 2.2 lb
 0.45 kg 
$1.10
= $0.495 per pound
2.2
 1T 
48. a) 1.3 t = (1.3 t ) 
 = 1.4 ≈ 1.44 T
 0.9 t 
 2000 lb 
b) 1.4 T = (1.4 T ) 
 = 2888.8 ≈ 2888.9 lb
 1T 
 1000 l   1 gal 
49. 34.5 kl = ( 34.5 kl ) 

 = 9078.947368 ≈ 9078.95 gal
 1 kl   3.8 l 
 28 g 
50. 0.25 oz = ( 0.25 oz ) 
=7 g
 1 oz 
$80
= 11.42857143 ≈ $11.43 per gram
7
 70 kg 
51. a) 8 stones = (8 stones ) 
 = 50.90 ≈ 50.91 kg
 11 stones 
 1 lb 
b) 50.90 kg = 50.90 kg 
 = 113.13 ≈ 113.13 lb
 0.45 kg 
(
52.
)
1
 1g 
carat = ( 0.125 carat ) 
 = 0.025 g
8
 5 carat 
 30 cm 
53. a) −282 ft = ( −282 ft ) 
 = −8460 cm
 1 ft 
 1m 
b) −8460 cm = ( −8460 cm ) 
 = −84.6 m
 100 cm 
287
288 CHAPTER 8 The Metric System
 1 qt 
54. 5.7 l = ( 5.7 l ) 
 = 6 qt
 0.95 l 
 ( 3.3)2 ft 2 
 = 10.89 ft 2
55. a) 1 m 2 = (1 m 2 ) 
 1 m2 


 ( 3.3)3 ft 3 
 = 35.937 ft 3
b) 1 m = (1 m ) 
 1 m3 


3
3
 ( 30 ) 2 cm 2
56. a) 1 ft 2 = (1 ft 2 ) 
 1 ft 2


 = 900 cm 2


 ( 30 )3 cm3 
 = 27 000 cm3
b) 1 ft 3 = (1 ft 3 ) 
 1 ft 3



 0.45 kg   1 mg 
57. 56 lb = ( 56 lb ) 
 = 25.2 mg

 1 lb   1 kg 
 0.45 kg   1.5 mg 
58. 170 lb = (170 lb ) 
 = 114.75 mg

 1 lb   1 kg 
 0.45 kg   200 mg 
59. 76 lb = ( 76 lb ) 
 = 6840 mg

 1 lb   1 kg 
 1g 
6840 mg = ( 6840 mg ) 
 = 6.84 g
 1000 mg 
 0.45 kg   5 mg 
60. 82 lb = ( 82 lb ) 
 = 184.5 mg

 1 lb   1 kg 
 12.5 mg 
61. a) 2 teaspoons = ( 2 teaspoons ) 
 = 25 mg
 1 teaspoon 
 30 ml  12.5 mg 
b) 12 fl oz = (12 fl oz ) 

 = 900 mg
 1 fl oz  5 ml 
 236 mg 
62. a) 2 tablespoons = ( 2 tablespoons ) 
 = 472 mg
 1 tablespoon 
 30 ml   1 tablespoon   236 mg 
b) 8 fl oz = ( 8 fl oz ) 
 = 3776 mg


 1 fl oz   15 ml
  1 tablespoon 
 30 cm   1 m 
63. a) 964 ft = ( 964 ft ) 

 = 289.2 m
 1 ft   100 cm 
 0.9 tonne 
b) 85, 000 tons = ( 85, 000 tons ) 
 = 76 500 t
 1 ton 
 1.6 km 
c) 28 mi = ( 28 mi ) 
 = 44.8 kph
 1 mi 
SECTION 8.4
64.
( 0.5 c ) 
0.24 l 
 = 0.12 l graham cracker crumbs
 1c 
(12 oz ) 
28 g 
 = 336 g nuts
 1 oz 
(8 oz ) 
28 g 
 = 224 g chocolate pieces
 1 oz 
 4  0.24 l 
 c 
 = 0.32 l flaked coconut
 3  1 c 
 4  0.24 l 
 c 
 = 0.32 l condensed milk
 3  1 c 
( 9 in.) 
2.54 cm 
 2.54 cm 
 × (13 in.) 
 = 22.86 cm × 33.02 cm baking pan
 1 in. 
 1 in. 
350° F =
5
( 350 − 32 ) = 176.6 ≈ 176.7° C
9
(1.5 in.) 
2.54 cm 
 2.54 cm 
 × ( 3 in.) 
 = 3.81 cm × 7.62 cm bars
 1 in. 
 1 in. 
65. a)
( 37 m ) 
1 yd 
 = 41. 1 ≈ 41.1 yd
0.9
m

 1 mi 
140 km ) 
 = 231,337.5 mi
 1.6 km 
b)
( 370
c)
( 44 km ) 
1 mi 
 = 27.5 mi
 1.6 km 
9
(1260 ) + 32 = 2300° F
5
d) 1260° C =
e)
( 335 km ) 
1 mi 
 = 209.375 mph
 1.6 km 
f)
( 29
g)
( 4.5 m ) 
 1 lb 
484 kg ) 
 = 65,520 lb
 0.45 kg 
1 yd 
 1 yd 
 × (18 m ) 
 = 5 yd × 20 yd
 0.9 m 
 0.9 m 
 1 gal 
h) (171 396 l ) 
 = 45,104.21053 ≈ 45,104.21 gal/min
 3.8 l 
 1 gal 
588 l ) 
 = 16, 733.68421 ≈ 16, 733.68 gal/min
 3.8 l 
i)
( 63
j)
( 46.89 m ) 
k)
(8.4 m ) 
l)
( 632
1 yd 
 = 52.1 yd
0.9
m

1 yd 
 = 9.3 ≈ 9.33 yd
 0.9 m 
 1 lb 
772 kg ) 
 = 1, 406,160 lb
 0.45 kg 
289
290 CHAPTER 8 The Metric System
 1 lb 
65. m) (106 142 kg ) 
 = 235,871. 1 ≈ 235,871.11 lb
 0.45 kg 
n) −251° C =
9
( −251) + 32 = −419.8° F
5


 1 grain   1 ml 
66. ( 0.2 mg ) 
 = 1.0 cc, or b)

 60 mg   1 grain 
 300

67. 15 (130 lb ) = 1950 lb
0.18 kg   1 lb 
 = 7.8 lb

 100 lb   0.45 kg 
(1950 lb ) 
68. a)
b)
69.
71.
73.
75.
1000 ml   1 cm3 
 = 4000 cc

 1 l   1 ml 
( 4.0 l ) 


4000
=
= 244.0949764 ≈ 244.09 in.3
3 
16.387064
 ( 2.54 ) cm 
( 4000 cm ) 
3
1 in.3
3
A meter
A hectare
A tonne
wonton
77. 1 kilohurtz
79. 1 megaphone
81. 2 kilomockingbird
83. 1 decoration
Review Exercises
1
1.
of base unit
100
4. 100 × base unit
7. 20 cg = 0.20 g
10. 1 000 000 mg = 1 kg
13. 2.67 kl = 2 670 000 ml
14 630 cl = 146 300 ml
3000 ml, 14 630 cl, 2.67 kl
16.
19.
22.
25.
28.
31.
Grams
Square meters
Kilograms or tonnes
a) and b) Answers will vary.
b
a
70.
72.
74.
76.
A kilogram
A liter
A decimeter
1 microscope


 28 g 
78. 1 pound cake 1 lb = 16 oz; 16 oz 
 = 448 g 
 1 oz 


80. 2 megacycles
82. 1 decacards
84. 1 microfiche
2. 1000 × base unit
5. 10 times base unit
8. 3.2 l = 320 cl
11. 4.62 kl = 4620 l
14. 0.047 km = 47 m
47 000 cm = 470 m
0.047 km, 47 000 cm,
4700 m
17. Degrees Celsius
20. Milliliters or cubic centimeters
23. Kilometers
26. a) and b) Answers will vary.
29. c
32. b
3.
1
of base unit
1000
1
of base unit
10
9. 0.0004 cm = 0.004 mm
12. 192.6 dag = 19 260 dg
15. Centimeters
6.
18.
21.
24.
27.
30.
Millimeters or centimeters
Millimeters
Meters or centimeters
c
a
REVIEW EXERCISES
 1 lb   1 T   0.9 t 
33. 2500 kg = ( 2500 kg ) 


 = 2.5 t
 0.45 kg   2000 lb   1 T 
 1 T  2000 lb   0.45 kg   1000 g 
34. 6.3 t = ( 6.3 t ) 
 = 6 300 000 g



 0.9 t  1 T   1 lb   1 kg 
35. 18° C =
9
(18 ) + 32 = 64.4° F
5
36. 68° F =
5
( 68 − 32 ) = 20° C
9
37. −6° F =
5
( −6 − 32 ) = −21. 1 ≈ −21.1° C
9
38. 39° C =
9
( 39 ) + 32 = 102.2° F
5
39. l = 4 cm, w = 1.6 cm
A = lw = 4 (1.6 ) = 6.4 cm 2
40. r = 1.5 cm
A = π r 2 ≈ 3.14 (1.5 ) = 7.065 ≈ 7.07 cm 2
2
41. a) V = lwh = (10 )( 4 )( 2 ) = 80 m3
b)
1000 l  1 kg 
(80 m )  11mkl 


 = 80
 1 kl  1 l 
3
3
000 kg
42. a) A = lw = 30 ( 22 ) = 660 m 2
 1 km 2
b) 660 m 2 = ( 660 m 2 ) 
 (1000 )2 m 2


 = 0.000 66 km 2


43. a) V = lwh = ( 80 )( 40 )( 30 ) = 96 000 cm3
 1 m3

 = 0.096 m3
b) 96 000 cm3 = ( 96 000 cm3 ) 
3
 (100 ) cm3 


 1 ml 
= 96 000 ml
c) 96 000 cm3 = ( 96 000 cm3 ) 
3 
 1 cm 
 1 kl 
d) 0.096 m3 = ( 0.096 m3 ) 
= 0.096 kl
3 
1 m 
44. Since 1 km = 100 ×1 dam, 1 km 2 = 100 2 × 1 dam 2 = 10 000 dam 2 .
Thus, 1 square kilometer is 10,000 times larger than a square dekameter.
45.
( 20 cm ) 
1 in. 
 = 7.874015748 ≈ 7.87 in.
 2.54 cm 
47.
 1 lb 
 = 233.3 ≈ 233.33 lb
 0.45 kg 
46.
(105 kg ) 
(83 yd ) 
48.
(100 m ) 
49.
( 45 mi ) 
1.6 km 
 = 72 kph
 1 mi 
50.
( 40 l ) 
51.
(15 gal ) 
 3.8 l 
 = 57 l
 1 gal 
52.
1 yd
( 40 m )  0.76
m
53.
(83 cm )  6.51 in.cm
54.
( 4 qt ) 
 0.9 m 
 = 74.7 m
 1 yd 
2


2
2

2
 = 12.76923077 ≈ 12.77 in.

1 yd 
 = 111. 1 ≈ 111.11 yd
 0.9 m 
1 qt 
 = 42.10526316 ≈ 42.11 qt
0.95
l

3


3
3

3
 = 52.63157895 ≈ 52.63 yd

 0.95 l 
 = 3.8 l
 1 qt 
291
292 CHAPTER 8 The Metric System

55.
m
(15 yd )  0.76
1 yd
57.
( 27 cm ) 
3
3
3


3
 = 11.4 m

1 ft 
 = 0.9 ft
30
 cm 
56.
( 62 mi ) 
1.6 km 
 = 99.2 km
 1 mi 
58.
( 3.25 in.) 
59. a) 700 (1.5 kg ) = 1050 kg
 1 lb 
b) 1050 kg = (1050 kg ) 
 = 2333.3 ≈ 2333.33 lb
 0.45 kg 
60. A = lw = ( 24 )(15) = 360 ft 2
 0.09 m 2 
2
360 ft 2 = ( 360 ft 2 ) 
 = 32.4 m
2
 1 ft 
61. a)
 3.8 l   1 kl 

 = 190 kl
 1 gal   1000 l 
( 50,000 gal ) 
 1000 l   1 kg 
b) (190 kl ) 

 = 190 000 kg
 1 kl   1 l 
 1.6 km 
62. a) 35 mi = ( 35 mi ) 
 = 56 kph
 1 mi 
 1000 m 
b) 56 km = ( 56 km ) 
 = 56 000 meters per hour
 1 km 
63. a) V = lwh = ( 90 )( 70 )( 40 ) = 252 000 cm3
 1 ml  1 l 
252 000 cm3 = ( 252 000 cm3 ) 
 = 252 l
3 
 1 cm  1000 ml 
 1 kg 
b) 252 l = ( 252 l ) 
 = 252 kg
 1l 
 1 lb 
64. 1 kg = (1 kg ) 
 = 2.2 lb
 0.45 kg 
$3.50
= $1.575 ≈ $1.58 per pound
2.2
Chapter Test
1. 204 cl = 0.204 dal
2. 123 km = 123 000 000 mm
 100 dam 
3. 1 km = (1 km ) 
 = 100 dam or 100 times greater
 1 km 
4. 400 ( 6 ) = 2400 m
5. b
( 2400 m ) 
1 km 
 = 2.4 km
 1000 m 
6. a
8. c
7. c
9. b
2.54 cm   10 mm 

 = 82.55 mm
 1 in.   1 cm 
GROUP PROJECTS
 1002 cm 2
10. 1 m 2 = (1 m 2 ) 
2
 1m

2
 = 10 000 cm or 10,000 times greater

 10003 mm3 
3
11. 1 m3 = (1 m3 ) 
 = 1 000 000 000 mm or 1,000,000,000 times greater
3
1
m


 2.54 cm 
12. 452 in. = ( 452 in.) 
 = 1148.08 cm
 1 in. 
 1 yd 
13. 150 m = (150 m ) 
 = 166.6 ≈ 166.67 yd
 0.9 m 
14. −10° F =
5
( −10 − 32 ) = −23.3 ≈ −23.33° C
9
15. 20° C =
9
( 20 ) + 32 = 68° F
5
 30 cm 
 12 in.  2.54 cm 
16. 12 ft = (12 ft ) 
 = 360 cm or 12 ft = (12 ft ) 

 = 365.76 cm
 1 ft 
 1 ft  1 in. 
17. a) V = lwh = 20 ( 20 )( 8 ) = 3200 m3
 1000 l 
 1 kl 
b) 3200 m3 = ( 3200 m3 ) 
= 3 200 000 l or 3 200 000 l = ( 3 200 000 l ) 
 = 3200 kl
3 
 1m 
 1000 l 
 1 kg 
c) 3 200 000 l = ( 3 200 000 l ) 
 = 3 200 000 kg
 1l 
18. Total surface area: 2lh + 2 wh = 2 ( 20 )( 6 ) + 2 (15)( 6 ) = 420 m 2
 1l 
Liters needed for first coat: ( 420 m 2 ) 
= 42 l
2 
 10 m 
 1l
Liters needed for second coat: ( 420 m 2 ) 
2
 15 m
Total liters needed: 42 + 28 = 70 l
 $3.50 
Total cost: ( 70 l ) 
 = $245
 1l 
Group Projects
1. a)
0.45 kg   20 mg 
 = 1764 mg

 1 lb   1 kg 
(196 lb ) 
 250 cc   1 hr 
b) 

 = 4.16 ≈ 4.17 cc/min
 1 hr   60 min 

 = 28 l

293
294 CHAPTER 8 The Metric System
2. a)
( 60 lb ) 
0.45 kg 
 = 27 kg
 1 lb 
Child's dose:
b)
27 kg
( 70 mg ) = 28 mg
67.5 kg
child's weight in kg
× 70 mg = 70 mg
67.5 kg
child's weight in kg
=1
67.5 kg
 1 lb 
Child's weight: 67.5 kg = ( 67.5 kg ) 
 = 150 lb
 0.45 kg 
3. a) 5 ft 2 in. = 62 in.
 2.54 cm 
62 in. = ( 62 in.) 
 = 157.48 cm
 1 in. 
 $1 U.S. 
b) 8695.5 yen = ( 8695.5 yen ) 
 = $73.53488372 U.S. ≈ $73.53 U.S.
 118.25 yen 
 16 oz   28g 
c) 6 lb = ( 6 lb ) 

 = 2688 g
 1 lb   1 oz 
 10 pesos   $0.095 U.S. 
2688 g = ( 2688 g ) 

 = 25.536 ≈ $25.54
 100 g   1 peso 
Note: If you use different conversion factors, your answer will be slightly different because the conversion
factors are rounded values.
d) To fill the tank in New Zealand dollars:
 $0.929 New Zealand 
53 l 
 = $49.237 New Zealand ≈ $49.24 New Zealand
1l


To fill the tank in U.S. dollars:
 $0.584 U.S. 
$49.237 New Zealand = ( $49.237 New Zealand ) 
 = $28.754408 U.S. ≈ $28.75 U.S.
 $1 New Zealand 
$28.754408 U.S. for 53 l
$28.754408 U.S.
= $0.542536 U.S. per l
53 l
 $0.542536 U.S.   3.8 l 
 = $2.0616368 U.S. per gal ≈ $2.06 U.S. per gal


1l

  1 gal 