# The A to Z of mathematics a basic guide - Sidebotham T.H.

ISBN 0-471-15045-2

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METRIC UNITS 285

References: Axis of Symmetry, Bisect, Center of a Circle, Line Segment, Locus, Perpendicular Bisector, Right Angle.

METER

The abbreviation of meter is m. The meter is the basic unit of length in the SystÃ¨me International dâ€™UnitÃ©s, abbreviated SI units. In 1983 the standard for the length of 1 meter was defined to be the length of the path traveled by light in a vacuum during a time interval 1/299,792,458 of a second.

The lengths equivalent to 1 meter in the imperial system of units are 39.3700 inches, 3.2808 feet, and 1.0936 yards, to four decimal places.

In athletic events the lengths of races are measured in meters, and distances thrown and jumped in the field events are measured in meters.

References: CGS System of Units, Imperial System of Units, Metric Units, SI Units.

METRIC UNITS

The metric unit most commonly used to measure length is the meter (m), to measure capacity is the liter (1), and to measure mass is the gram (g) (mass is often incorrectly called weight).

Using the prefixes milli (division by 1000) and kilo (multiplication by 1000), we form other metric units that are related to meter, liter, and gram. There are other prefixes (see SI Units) and one that is frequently used is centi (division by 100). We now look at the relationships among different units of length, area, capacity, volume, and mass.

Length The units of length are:

â™¦ Millimeter (mm), which is 1 meter (m) divided by 1000, or 1 centimeter divided by 10

â™¦ Centimeter (cm), which is 1 meter divided by 100

â™¦ Kilometer (km), which is 1 meter multiplied by 1000

286 METRIC UNITS

Examples:

â™¦ Millimeters are used to measure very small distances, like the length of your fingernail, say 8 mm.

â™¦ Centimeters are used to measure small distances, like the length of your arm, say 23 cm.

â™¦ Meters are used to measure medium-sized distances, like your height, say 1.7 m.

â™¦ Kilometers are used to measure long distances, like that between towns, say 27 km.

Example. Convert the length of a roadway of 3.5 km into centimeters.

Solution. The first step is to change 3.5 km into meters by multiplying the number of kilometers by 1000:

3.5 km x 1000 = 3500 m

The second step is to change 3500 m into centimeters by multiplying the number of meters by 100:

3500 x 100 = 350,000 The length of the roadway is 350,000 cm.

Area The units of area are:

â™¦ Square millimeter (mm2), which is a square that measures 1 mm by 1 mm.

â™¦ Square centimeter (cm2), which is a square that measures 1 cm by 1 cm, or 10 mm by 10 mm.

â™¦ Square meter (m2), which is a square that measures 1 m by 1 m, or 100 cm by 100 cm.

â™¦ Square kilometer (km2), which is a square that measures 1 km by 1 km, or 1000 m by 1000 m.

â™¦ Hectare (ha), which is equivalent to an area of 10,000 m2, and is a square that measures 100 m by 100 m. There are 100 ha in 1 km2.

Examples:

â™¦ Square millimeters are used to measure very small areas, like the area of your fingernail, say 40 mm2.

â™¦ Square centimeters are used to measure small areas, like the area of a page of a book, say 300 cm2.

METRIC UNITS 287

â™¦ Square meters are used to measure medium-sized areas, like the area of a garden, say 950 m2.

â™¦ Square kilometers are used to measure large areas, like the area of a country, for example, 9,363,169 km2 is the area of the United States.

â™¦ Hectares are used to measure fairly large areas, like the area of a farm, 800 ha.

Example. Convert the area of a farm of 800 ha into square kilometers.

Solution. There are 100 ha in 1 km2. Write

800 -r- 100 = 8

The area of the farm is 8 km2.

Capacity This is the volume of liquid that a container holds. The units of capacity

are:

â™¦ Milliliter (ml), which is a cube that measures 1 cm by 1 cm by 1 cm, or 10 mm by 10 mm by 10 mm (remember that a capacity of 1 ml is the same as the volume of 1 cm3.)

â™¦ Liter (1), which is a cube that measures 10 cm by 10 cm by 10 cm.

â™¦ Kiloliter (kl), which is a cube that measures 1 m by 1 m by 1 m, or 100 cm by 100 cm by 100 cm.

Examples:

â™¦ Milliliters are used to measure very small capacities, for example, 1.5 ml of ink in a ballpoint pen, or 5 ml of medicine in a full teaspoon.

â™¦ Liters are used to measure medium capacities, like the quantity of water in a bath, say 830 liters.

â™¦ Kiloliters are used to measure large capacities, like the quantity of water in a lake, say 300,000 kiloliters.

The relationships between them are

1000 ml = 11 10001= 1 kl

1,000,000 ml = lkl

Example. A jug holds 2.3 1 of milk. Convert this capacity into milliliters.

288 METRIC UNITS

Solution. We multiply the 2.3 1 by 1000 to change it into milliliters:

2.3 x 1000 = 2300

The jug holds 2300 ml.

Volume The units of volume are:

â™¦ Cubic millimeter (mm3), which is a cube that measures 1 mm by 1 mm by 1 mm.

â™¦ Cubic centimeter (cm3), which is a cube that measures 1 cm by 1 cm by 1 cm.

â™¦ Cubic meter (m3), which is a cube that measures 1 m by 1 m by 1 m.

Examples:

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