Prealgebra: Measurements: Systems of Measurement

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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 English 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 Metric System

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

Converting Measurements

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: