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# Metric system

The metric system is a system of measurement developed during the French Revolution and based on permanent natural standards rather than on royal decrees. Joseph Lagrange headed the Revolutionary weights-and-measures committee that developed it and set its initial definitions.

Traditional systems of measurement all used standard lengths of parts of the human body, or standard distances that a human might walk. The metric system, by contrast, initially used the earth itself as the ultimate standard.

Today the conventions of the metric system survive, but the fundamental definitions of the individual units of measurement have changed and are largely superseded by the conventions of the International System of Units.

## Definitions

All measurement systems must start with one basic unit. For the metric system, this unit is the meter. Every other named unit of the metric system had a definition that depended upon it.

### Prefixes

All base units of the metric system have prefixes that multiply, or divide, the unit by various factors of ten (or alternatively, a thousand). They are:

The prefix: Multiplies the unit by:
atto- 10-18
femto- 10-15
pico- 10-12
nano- 10-9
micro- (Greek small) 10-6
milli- (Latin one thousand) 10-3
centi- (Latin one hundred) 10-2
deci- (Latin ten) 10-1
deka- (Greek ten) 101
hecto- (Greek one hundred) 102
kilo- (Greek one thousand) 103
mega- (Greek large) 106
giga- (Latin gigantic) 109
tera- (Greek wonder) 1012

Other, related systems (see below) use the same prefixes to multiply their units.

### Length

The base unit of length, and originally the unit from which all other definitions flowed, is the meter. The original definition was "one ten-millionth the distance from the equator to the north pole." Lagrange's surveyors computed this distance (probably using a variation on Eratosthenes' tropical-shadow experiment) and inscribed it on a metal bar that they kept at the weights-and-measures headquarters building in Sèvres, France.

But this artifact, being made of metal, tended to expand and contract. Centuries later, when the scientific community realized what had happened, the task of re-standardizing all meter sticks to the equator-to-pole-times-10-7 definition was judged too onerous. Therefore the meter was redefined. At first it was defined as 1,650,763.73 wavelengths of the orange-red line in the excitation spectrum of krypton-86. Today it is defined as 1⁄299,792,458th of a light-second.

The meter in all its multiples replaces all other units of measurement, long and short. Long distance is measured in the meter multiplied by a thousand--the kilometer. Short distances are measured in centimeters--or millimeters, or micrometers, or however small one needs to measure them.

### Volume

The base unit of volume is the liter. Originally this was the volume of a cube that was one decimeter on an edge. Today the definition has changed, but only because the definition of length has changed, while the definition of mass (see below) has not. To understand what a standard liter is today (and why it is no longer exactly equal to one thousand cubic centimeters), one must turn to the definition of the unit of:

### Mass

The base unit of mass is the gram. Originally a gram was the mass of one cubic centimeter (see above), then called a milliliter, of water. The Lagrange committee fashioned an artifact exactly one thousand times as heavy as this--the volume, in short, of one liter of water--and stored this permanently at Sèvres.

Mass never changes. But in addition to the prototype meter changing its length over time, scientists later realized that water has different densities at different temperatures.

Today, the standard kilogram is kept at the International Bureau of Standards headquarters in Sevres. It remains today the only generally accepted unit of measurement based on an artifact. But the definition of the liter has now changed, and is no longer dependent on the length of the meter. Today, one liter is defined as the volume of one kilogram of water at four degrees Celsius. One milliliter is simply one-thousandth of this, and one milliliter of water at this temperature weighs one gram. But to say that one liter is "one thousand cubic centimeters" is no longer correct, simply because the definition of length has changed, while that of mass has not.

## Relation to other systems of measurement

The International System of Units borrows some definitions and concepts from the metric system--most notably the meter and the kilogram--and adds other definitions of other quantities, most notably time, force, amount of substance, plane angle, solid angle, and luminous intensity. The liter is not the unit of volume in that system, however.

In addition to the International System (or in French, Systèm International, or SI for short), scientists have invented other systems of measurement that include units of time, force, energy, and electric charge. The most popular are the meter-kilogram-second and centimeter-gram-second systems.

Various governing authorities have established conversion ratios to assist people in converting between the metric system and other, more traditional units of measurement.