To convert from one unit of length to another, unit fractions may be used. A unit fraction is a fraction that equals 1.

To convert 60 inches to feet, multiply by a unit fraction that relates feet to inches. The unit fraction should be written so that the units we are converting to, feet, are in the numerator and the original units, inches, are in the denominator.

Unit fractionunits converting to

original units

60 in. 1 ft

1 ft 12 in.

60 in. 1 ft

1 12 in.60

in.

60 1ft

1 12

60 ft5 ft

12

Converting Between Measurements

The basic unit of length in the metric system is the meter. A meter is slightly longer than a yard. It is approximately 39.37 inches long. Like the decimal system, the metric system uses powers of ten to define units.

Metric System of Measurement

Metric System of Measurement

Prefix kilo hecto deka

deci centi milli

Meaning 1000 100 10

1/10 1/100 1/1000

1 millimeter (mm) = 1/1000 or 0.001 m

1 centimeter (cm) = 1/100 or 0.01 m

1 decimeter (dm) = 1/10 or 0.1 m

1 meter (m) = 1 m

1 dekameter (dam) = 10 m

1 hectometer (hm) = 100 m

1 kilometer (km) = 1000 meters (m)

Metric Unit of Length

Metric System of Measurement

The most commonly used measurements of length in the metric system are the meter, millimeter, centimeter, and kilometer.

Metric System of Measurement

As with the U.S. system of measurement, unit fractions may be used to convert from one unit of length to another. The major advantage of the metric system is the ease of converting from one unit of length to another. Since all units of length are powers of 10 of the meter, converting from one unit of length to another is as simple as moving the decimal point.

Converting Between Measurements

Listing units of length in order from largest to smallest helps keep track of how many places to move the decimal point when converting.

km hm dam m dm cm mm

Using the listing of units of length, convert 3.5 m to centimeters.

Start End

2 units to the right

3.50 m = 350. cm or 350 cm

2 places to the right

Converting Between Measurements

The prefixes for units of mass in the metric system are the same as for units of length.

Metric System of Measurement

Prefix kilo hecto deka

deci centi milli

Meaning 1000 10010

1/10 1/100 1/1000

1 milligram (mg) = 1/1000 or 0.001 g

1 centigram (cg) = 1/100 or 0.01 g

1 decigram (dg) = 1/10 or 0.1 g

1 gram (g) = 1 g

1 dekagram (dag) = 10 g

1 hectogram (hg) = 100 g

1 kilogram (kg) = 1000 grams (g)

Metric Unit of Length

Mass – Metric System

The three most commonly used units of mass in the metric system are the milligram, the gram, and the kilogram.

As with length, all units of mass are powers of 10 of the gram, so converting from one unit of mass to another only involves moving the decimal point.

kg hg dag g dg cg mg

StartEnd

2 units to the leftUsing the listing of units of mass, convert 4.75 cg to grams.

04.75 cg = 0.0475 g

2 places to the left

Mass – Metric System

Examples

Use unit multipliers to convert the following:

① 58 meters to centimeters

② 1000 meters to kilometers

③ 48,000 milligrams to grams

④ 486 kilograms to grams

⑤ 538 centimeters to meters