Basic Mathematics for College Students

Chapter 5 Summary and Review 491

SECTION 5.5 Converting between American and Metric Units

We convert between American and metric

unitsof length using the facts on the right. In all

but one case, the conversions are rounded

approximations.

DEFINITIONS AND CONCEPTS EXAMPLES

American to metric Metric to American

1 mi1.61 km 1 km0.62 mi

1 yd0.91 m 1 m1.09 yd

1 ft0.30 m 1 m3.28 ft

1 in.2.54 cm 1 cm0.39 in.

Unit conversion factorscan be formed from the

facts in the tables on the right to make specific

conversions between American and metric

units of length.

Convert 15 inches to centimeters.

To convert from inches to centimeters, we select a unit conversion

factor that introduces the units of centimeters and eliminates the units

of inches. Since there are 2.54 centimeters for every inch, we will use:

To perform the conversion, we multiply.

Write 15 in. as a fraction.

Then multiply by a form of 1:.

Simplify.

Do the multiplication.

Thus, 15 inches = 38.1 centimeters.

 38.1 cm

 15 2.54 cm

Remove the common units of inches

from the numerator and denominator.

The units of cm remain.



15 in.

1



2.54 cm

1 in.

2.54 cm

1 in.^

15 in.

15 in.

1



2.54 cm

1 in.

This is the unit we want to introduce.

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

2.54 cm

1 in.

We convert between American and metric

unitsof mass (weight) using the facts on

the right. The conversions are rounded

approximations.

American to metric Metric to American

1 lb0.45 kg 1 kg2.20 lb

1 oz28.35 g 1 g0.035 oz

Unit conversion factorscan be formed from the

facts in the tables on the right to make specific

conversions between American and metric

units of mass (weight).

Convert 6 kilograms to ounces.

There is not a single unit conversion factor that converts from

kilograms to ounces. We must use two unit conversion factors.One to

convert kilograms to grams, and another to convert that result to

ounces.

Simplify.

Do the multiplication.

Thus, 6 kilograms210 ounces.

210 oz

Multiply the last two factors:

 6 35 oz 1,0000.03535.

 6 1,0000.035 oz

Remove the common units of

kilograms and grams in the

numerator and denominator.

The units of oz remain.



6 kg

1



1,000 g

1 kg



0.035 oz

1 g

6 kg

6 kg

1



1,000 g

1 kg



0.035 oz

1 g