1. Chapter 1 / Whole Numbers and Introduction to Algebra
Converting Between Measurements
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 fraction
units converting to
60 in.
original units

2. Chapter 1 / Whole Numbers and Introduction to Algebra
Metric System of Measurement
The basic unit of length in the metric system is the meter. A meter is slightly longer than a yard. It is approximately inches long. Like the decimal system, the metric system uses powers of ten to define units.

3. 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 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

4. Chapter 1 / Whole Numbers and Introduction to Algebra
Metric System of Measurement
The most commonly used measurements of length in the metric system are the meter, millimeter, centimeter, and kilometer.

5. Chapter 1 / Whole Numbers and Introduction to Algebra
Converting Between Measurements
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.

6. 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.
Start
End
km hm dam m dm cm mm
2 units to the right
Using the listing of units of length, convert 3.5 m to centimeters.
3.50 m
= 350. cm or 350 cm
2 places to the right

7. 1 kilogram (kg) = 1000 grams (g)
Mass – Metric System
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
100 10
1/10 1/100 1/1000
1 milligram (mg) = 1/1000 or 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

8. Chapter 1 / Whole Numbers and Introduction to Algebra
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.
End
Start
kg hg dag g dg cg mg
2 units to the left
Using the listing of units of mass, convert 4.75 cg to grams.
04.75 cg
= g
2 places to the left

9. Examples Use unit multipliers to convert the following:
58 meters to centimeters
1000 meters to kilometers
48,000 milligrams to grams
486 kilograms to grams
538 centimeters to meters