Basic Mathematics for College Students

We can convert between American units of weight and metric units of mass using
the rounded approximations in the following table.

5.5 Converting between American and Metric Units 471

Self Check 2

TRACK AND FIELD Which is

longer: a 500-meter race or a

550-yard race?

Now TryProblem 17

To perform the conversion, we multiply.

Write 82 cm as a fraction:.

Multiply by a form of 1:.

Simplify.

Do the multiplication.

Round to the nearest inch (ones column).

To the nearest inch, the waist size is 32 inches.

32 in.

31.98 in.

 82 0.39 in.

Remove the common units of centimeters from the

 numerator and denominator. The units of inches remain.

82 cm

1



0.39 in.

1 cm

0.39 in.

1 cm

82 cm82 cm 1

82 cm

82 cm

1



0.39 in.

1 cm

0.39

 82

78

3120

31.98

EXAMPLE (^2) Mountain Elevations Pikes Peak, one of the most
famous peaks in the Rocky Mountains, has an elevation of 14,110 feet. The
Matterhorn, in the Swiss Alps, rises to an elevation of 4,478 meters. Which
mountain is higher?
StrategyWe will convert the elevation of Pikes Peak, which given in feet, to
meters.
WHYThen we can compare the mountain’s elevations in the same units, meters.
Solution
To convert Pikes Peak elevation from feet to meters we must choose a unit
conversion factor whose numerator contains the units we want to introduce
(meters) and whose denominator contains the units we want to eliminate (feet).
From the second row of the American to metriccolumn of the table, we see that
there is approximately 0.30 meter per foot. Thus, we will use the unit conversion
factor:
To perform the conversion, we multiply.
Write 14,110 ft as a fraction:.
Multiply by a form of 1:.
Simplify.
Do the multiplication.
Since the elevation of Pikes Peak is about 4,233 meters, we can conclude that the
Matterhorn, with an elevation of 4,478 meters, is higher.
4,233 m
14,1100.30 m
Remove the common units of feet from
the numerator and denominator. The
units of meters remain.



14,110 ft

1



0.30 m

1 ft

0.30 m

1 ft

14,110 ft14,110 ft 1

14,110 ft

14,110 ft

1



0.30 m

1 ft

This is the unit we want to introduce.

 This is the unit we want to eliminate (the original unit).

0.30 m

1 ft

Equivalent Weights and Masses

American to metric Metric to American

1 oz 28.35 g 1 g 0.035 oz

1 lb 0.45 kg 1 kg 2.20 lb

1 pound

1 kilogram

1

1

4,110

0.30

000 00

4233 00

4233.00