1.1 Starting with the definition 1 in. = 2.54 cm, find the number of (a) kilometers in 1.00 mile
and (b) feet in 1.00 km.
a.
1.00 mi x
where 1 mi = 63,360 in
63,360 𝑖𝑛
b.
1.00 km x
2.54 𝑐𝑚
x
1.0 𝑚𝑖
1 𝑘𝑚
x 100,000 𝑐𝑚 = 1.609 km or 1.61 km
1 𝑖𝑛
where 1ft = 12 in
100,000 𝑐𝑚
1 𝑘𝑚
1 𝑖𝑛
1 𝑓𝑡
x 2.54 𝑐𝑚 x 12 𝑖𝑛 = 3,280.84 or 3.28 x 103 ft
1.2 According to the label on a bottle of salad dressing, the volume of the contents is 0.473 liter
(L). Using only the conversions 1 L = 1000 cm3 and 1 in. = 2.54 cm, express this volume in
cubic inches.
0.473 L x
1000 𝑐𝑚3
1𝐿
1 𝑖𝑛
3
x (2.54 𝑐𝑚) = 28.9 in3
1.4 The density of gold is 19.3 g/cm3. What is this value in kilograms per cubic meter?
𝑔
100 𝑐𝑚 3
1 𝑘𝑔
19.3𝑐𝑚3 x 1000 𝑔 x (
1𝑚
𝑘𝑔
𝑘𝑔
) = 19,300 𝑚3 or 1.93 x 104𝑚3
1.5 The most powerful engine available for the classic 1963 Chevrolet Corvette Sting Ray
developed 360 horsepower and had a displacement of 327 cubic inches. Express this
displacement in liters (L) by using only the conversions 1 L = 1000 cm3 and 1 in. = 2.54 cm.
2.54 𝑐𝑚 3
327 in3 x (
1 𝑖𝑛
1𝐿
) x 1000 𝑐𝑚3 = 5.36 L
1.6 A square field measuring 100.0 m by 100.0 m has an area of 1.00 hectare. An acre has an
area of 43,600 ft2. If a country lot has an area of 12.0 acres, what is the area in hectares?
1.0 hectare = 100.0 m x 100.0 m = 10,000 m2
where 1 ft = 0.305 m
12.0 acres x
43,600 ft2
1 𝑎𝑐𝑟𝑒
0.305 𝑚 2
x(
1 𝑓𝑡
1 hectare
) x 10,000 𝑚2 = 4.87 hectare
1.7 How many years older will you be 1.00 gigasecond from now? (Assume a 365-day year.)
1.00 Gs x
1.0 𝑥 109 𝑠
1 𝐺𝑠
x
1 𝑚𝑖𝑛
60 𝑠
1ℎ
1𝑑
1𝑦
x60 𝑚𝑖𝑛 x 24 ℎ x 365 𝑑 = 31.7 y
1.9 A certain fuel-efficient hybrid car gets gasoline mileage of 55.0 mpg (miles per gallon). (a) If
you are driving this car in Europe and want to compare its mileage with that of other European
cars, express this mileage in km/L (L = liter). Use the conversion factors in Appendix E. (b) If
this car’s gas tank holds 45 L, how many tanks of gas will you use to drive 1500 km?
a. where 1 mi = 1.609 km
1 gallon = 3.788 L
𝑚𝑖
55.0 𝑔𝑎𝑙𝑙𝑜𝑛 x
1.609 𝑘𝑚
1 𝑚𝑖
x
1 𝑔𝑎𝑙𝑙𝑜𝑛
3.788 𝐿
= 23.4
b.
1500 km x
1𝐿
23.4 𝑘𝑚
x
1 𝑡𝑎𝑛𝑘
45 𝐿
= 1.4 tanks
𝑘𝑚
𝐿