Metric or SI (Le **S**ystème **I**nternational d'Unités) units are based on units of ten. Very large or very small numbers are easier to work with when you can replace any scientific notation with a name or word. The metric unit prefixes are short words that indicate a multiple or fraction of a unit. The prefixes are the same no matter what the unit is, so decimeter means 1/10th of a meter and deciliter means 1/10th of a liter, while kilogram means 1000 grams and kilometer means 1000 meters.

Decimal-based prefixes have been used in all forms of the metric system, dating back to the 1790s. The prefixes used today have been standardized from 1960 to 1991 by the International Bureau of Weights and Measures for use in the metric system and the International System of Units (SI).

## Examples Using Metric Prefixes

The distance from City A to City B is 8.0 x 10^{3} meters. From the table, 10^{3} can be replaced with the prefix 'kilo'. Now the distance could be stated as 8.0 kilometers or shortened further to 8.0 km.

The distance from Earth to the Sun is approximately 150,000,000,000 meters. You could write this as 150 x 10^{9} m, 150 gigameters or 150 Gm.

The width of human hair runs on the order of 0.000005 meters. Rewrite this as 50 x 10^{-6}m, 50 micrometers, or 50 μm.

## Metric Prefixes Chart

This table lists common metric prefixes, their symbols, and how many units of ten each prefix is when the number is written out.

Prefix |
Symbol |
x from 10^{x} |
Full Form |

yotta | Y | 24 | 1,000,000,000,000,000,000,000,000 |

zetta | Z | 21 | 1,000,000,000,000,000,000,000 |

exa | E | 18 | 1,000,000,000,000,000,000 |

peta | P | 15 | 1,000,000,000,000,000 |

tera | T | 12 | 1,000,000,000,000 |

giga | G | 9 | 1,000,000,000 |

mega | M | 6 | 1,000,000 |

kilo | k | 3 | 1,000 |

hecto | h | 2 | 100 |

deca | da | 1 | 10 |

base | 0 | 1 | |

deci | d | -1 | 0.1 |

centi | c | -2 | 0.01 |

milli | m | -3 | 0.001 |

micro | μ | -6 | 0.000001 |

nano | n | -9 | 0.000000001 |

pico | p | -12 | 0.000000000001 |

femto | f | -15 | 0.000000000000001 |

atto | a | -18 | 0.000000000000000001 |

zepto | z | -21 | 0.000000000000000000001 |

yocto | y | -24 | 0.000000000000000000000001 |

## Interesting Metric Prefix Trivia

Not all of the metric prefixes that were proposed were adopted. For example, myria- or myrio- (10^{4}) and the binary prefixes double- (factor of 2) and demi- (one-half) were originally used in France in 1795, but were dropped in 1960 because they were not symmetrical or decimal.

The prefix hella- was proposed in 2010 by UC Davis student Austin Sendek for one octillion (10^{27}). Despite receiving significant support, the Consultative Committee for Units rejected the proposal. Some websites did, however, adopt the prefix, notably Wolfram Alpha and Google Calculator.

Because the prefixes are based on units of ten, you don't have to use a calculator to perform conversions between different units. All you need to do is move the decimal point to the left or right or add/subtract exponents of 10 in scientific notation.

For example, if you want to convert millimeters to meters, you can move the decimal point three places to the left: 300 millimeters = 0.3 meters

If you have trouble trying to decide which direction to move a decimal point, use common sense. Millimeters are small units, while a meter is large (like a meter stick), so there should be lots of millimeters in a meter.

Converting from a large unit to a smaller unit works the same way. For example, converting kilograms to centigrams, you move the decimal point 5 places to the right (3 to get to the base unit and then 2 more): 0.040 kg = 400 cg