There are a number of different systems of measurement. Here we will look at the two most common, the English system and the Metric system.

The units of measurement in the English system are:

*Length/Area*

1 foot (ft) = 12 inches (in)

1 yard (yd) = 3 feet

1 mile (mi) = 1,760 yards

1 square foot (sq ft) = 144 square inches (sq in)

1 square yard (sq yd) = 9 square feet

1 acre = 4,840 square yards = 43,560 square feet

1 square mile (sq mi) = 640 acres

*Capacity*

1 tablespoon (T) = 3 teaspoons (t)

1 cup (c) = 16 tablespoons

1 pint (pt) = 2 cups

1 quart (qt) = 2 pints

1 gallon (gal) = 4 quarts

*Weight*

16 ounces (oz) = 1 pound (lb)

1 ton = 2,000 pounds

The units of measurement in the metric system are:

*Length*

1 millimeter (mm) = 0.001 meters (m)

1 centimeter (cm) = 0.01 m

1 decimeter (dm) = 0.1 m

1 meter (m) = 1 m

1 decameter (dam) = 10 m

1 hectometer (hm) = 100 m

1 kilometer (km) = 1,000 m

*Capacity*

1 milliliter (ml) = 0.001 liters (l)

1 centiliter (cl) = 0.01 l

1 deciliter (dl) = 0.1 l

1 liter (l) = 1 l

1 decaliter (dal) = 10 l

1 hectoliter (hl) = 100 l

1 kiloliter (kl) = 1,000 l

*Weight*

1 milligram (mg) = 0.001 grams (g)

1 centigram (cg) = 0.01 g

1 decigram (dg) = 0.1 g

1 gram (g) = 1 g

1 decagram (dag) = 10 g

1 hectogram (hg) = 100 g

1 kilogram (kg) = 1,000 g

We can convert measurements from one unit to another unit within the same system (English or Metric) or between the two systems. Let's say a piece of land is 2.3 square miles, but the contractor needs to know the area in acres. How would he convert the measurement?

To convert measurements, it is necessary to know conversion factors between measurements. A conversion factor is a clever way of writing 1 as a fraction in which the numerator is equal to the denominator but the numerator and the denominator have different units. For example, (1,000 m)/(1 km) is a conversion factor because 1,000 m = 1 km. (1 ft)/(12 in) is a conversion factor because 1 ft = 12 in.

An important fact to remember is that when fractions are multiplied, numbers in the
numerator and numbers in the denominator cancel out, as shown in
Fractions. Also, *units* in the numerator and
the denominator cancel out: if a unit appears in both the numerator and the denominator,
we can cross both units out. For example:

× = × = 5, 000 m

Using these two pieces of knowledge, here are the steps to converting a measurement
from one unit into another, using the example problem above of converting 2.3 square
miles into acres:

*Step 1.* Write down the given units as a fraction over 1.

=

and

× =

× = 1, 472 acres

To convert between English and Metric units, it is useful to know the following
conversion factors:

*Length/Area*

1 in = 2.540 cm

1 ft = 0.3048 m

1 mi = 1.609 km

1 sq ft = 0.0929 sq m

1 sq mi = 2.59 sq km

*Capacity*

1 fl oz = 29.575 ml

1 gal = 3.785 l

*Weight*

1 oz = 28.35 g

1 lb = 0.4536 kg

Here is an example of a conversion from metric units to English units: if Bob ran a 5.0
km race, how many miles did he run?

*Step 1.* Write down the given units as a fraction over 1.

=

and

× =

× = = 3.1075 mi