Systems of Measurement
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You can't have science without measurement, and measurement requires an agreed-upon set of standards. Almost the entire world uses the metric system, and in the United States we use the metric system for scientific work.

The metric system is formally known as the International Standard System or SI system. It works by defining base units for elementary properties such as length and mass. Other units are made up of combinations of base units, and are called derived units. Many of the derived units are named after scientists who made major contributions to our understanding of that particular quantity. The units have abbreviations that are usually a single letter, such as m for meter or g for gram. Capitalization is important in notation, so get used to paying attention to it.

Units can be modified by putting a metric prefix in front of them. Each metric prefix represents a power of 10. For example, kilo means one thousand, so a kilometer is 1000 meters. The prefixes are also abbreviated with a single letter, so a kilometer can be written as a km.

Common Prefixes

The metric system gives names to many different powers of ten, but in practice we only use a few. The engineering standard is to use every third power of ten, such as 103, 109, 1012, etc., and for small numbers 10-3, 10-6, etc. The only exception is the centimeter. "Cent" means a hundredth, or 10-2, but the centimeter is used because it is such a convenient unit for measuring length.

Here are the commonly used prefixes, along with their abbreviations. Note that the capitalization is very important—M means Mega, but m means milli. The symbol for micro is the lower-case Greek letter mu (m).

Giga (G) = 109
Mega (M) = 106
kilo (k) = 103
centi (c) = 10-2
milli (m) = 10-3
micro (m) = 10-6
nano (n) = 10-9
pico (p) = 10-12


The base unit for length is the meter, which is just a little bit more than a yard. The meter has gone through several different definitions, each one more precise than its predecessors. It was originally intended to be one ten-millionth of the distance from the equator to the North Pole along a line of longitude passing through Paris. This is not a useful definition in practice, because it would be too difficult to measure, so they kept a metal bar in Paris that had two lines scribed into it. The distance between these lines was the international definition of the meter. In the 1960s the meter was defined in terms of wavelengths of light, and in the 1980s it was redefined in terms of the speed of light. Some commonly used lengths are a meter (about a yard), a kilometer (about 0.6 miles), a centimeter (cm), which is a little less than half an inch, and a millimeter (mm), a little less than a sixteenth of an inch.


Volume should not need its own unit, because it is based on length. If the base unit for length is a meter, then the unit for area should be a square meter or m2, and the unit for volume should be a cubic meter or m3. A cubic meter is quite large, though, and so for practical reasons we use a unit of volume called a liter, which is about a quart. A liter is one-thousandth of a cubic meter. It is also 1000 cubic centimeters, which means that it would be a cube measuring 10 cm by 10 cm by 10 cm.

A cubic centimeter is a commonly used volume that goes by several names. According to the SI rules, a cubic centimeter should be abbreviated as cm3, but it is often written as a ‘cc’. Because a liter is a thousand cubic centimeters, a cubic centimeter is also a thousandth of a liter, or one mL. Thus we have three equivalent ways of abbreviating a cubic centimeter:

1 cm3 = 1 cc = 1 mL


The base unit for mass is the gram, which is a very small mass, about the same as a paper clip. Originally it was intended that a gram would be the weight of one cm3 (or 1 mL) of water. Although this is no longer the official definition, it is a very useful thing to remember:

The density of water is about 1 g / cm3, or 1 kg / L, or 1000 kg / m3.

This is not exact because the density of water varies with temperature and pressure, and to further complicate things most water has other stuff dissolved in it. 

Today the unit for mass is defined by a standard kilogram mass, which is kept in Paris. A kilogram weighs about 2.2 pounds.



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Copyright 2000-2001
  James W. Brennan
Selland College of Applied Technology
Boise State University

Last Updated 07/08/04 by JWB