The International Bureau of Weights and Measures has adopted a series of prefix names and symbols for decimal multiples and submultiples of SI units. They are expressed as powers of 10 and range from 10^{24} to 10^{-24}.

The advantages of basing the multiples and submultiples on the decimal system are:

- there are no fractions – decimals only
- there are no long rows of zeros – prefixes replace them
- they are unique, unambiguous letter symbols
- they eliminate the confusion of old number names – is a billion a thousand million (USA) or a million million (Europe)?

## SI prefixes

Larger and smaller quantities are expressed by using appropriate prefixes with the base unit. For example, the base unit of length is the metre. For small lengths, the millimetre (10^{-3} m) may be the appropriate quantity, whereas for large distances, the kilometre (10^{3} m) may be more appropriate.

These prefixes multiply base units for larger measurements: | These prefixes are decimal fractions that multiply base units for smaller measurements: | ||||

Prefix | Symbol | Multiple | Prefix | Symbol | Submultiple |
---|---|---|---|---|---|

yotta | Y | 10 | deci | d | 10 |

zetta | Z | 10 | centi | c | 10 |

exa | E | 10 | milli | m | 10 |

peta | P | 10 | micro |
| 10 |

tera | T | 10 | nano | n | 10 |

giga | G | 10 | pico | p | 10 |

mega | M | 10 | femto | f | 10 |

kilo | k | 10 | atto | a | 10 |

hecto | h | 10 | zepto | z | 10 |

deka | da | 10 | yocto | y | 10 |

10 |

The first letter of the SI abbreviation represents the prefix and the second letter represents the base unit.

- In the You, Me and UV context, information is given about the UV index. One unit on the UV index is roughly equivalent to 25 millijoules of UV energy falling per second on a 1 square metre area. In abbreviated form, this amount of energy is written as 25 mJ.
- In the Nanoscience context, it is reported that fingernails grow at about 1 nanometre per second. In abbreviated form, this length is written as 1 nm.
- The Space Revealed context deals with extremely large distances. For example, in the section on distances in space, it states: When the Space Shuttle goes into space, it orbits about 700 km above the surface of the Earth. The ‘km’ means kilometre, which is 10
^{3}m. The distance from the Earth to Mars is 78 million kilometres, which is 78 x 10^{6}km, and this in turn is 78 x 10^{9}m. Using the prefix for 10^{9}from the table above, this becomes 78 Gm, which is pronounced as ‘seventy-eight gigametres’.

## Prefix names

To many people, the choice of prefix names seems strange. For example, where does ‘kilo’ come from?

Prefix names have been mostly chosen from Greek words (positive powers of 10) or Latin words (negative powers of 10), although recent extensions of the range of powers of 10 has resulted in the use of words from other languages. ‘Kilo’ comes from the Greek word for 1000 (10^{3}), and ‘milli’ comes from the Latin word for one thousandth (10^{-3}

## Regular prefixes

Most of the prefixes in the table above are multiples of a thousand. These are referred to as regular prefixes and may be used with any SI unit.

Using metre as an example:

Multiples of the metre | Submultiples of the metre |
---|---|

1000 m = 1 km = 10 | 0.001 m = 1 mm =10 |

1000 km = 1 Mm =10 | 0.001 mm = 1 μm =10 |

1000 Mm = 1 Gm =10 | 0.001 μm = 1 nm =10 |

Prefixes are easier to write and pronounce than powers of 10. The following example shows the same quantity written in different ways. Which is easiest?

The average daily energy requirement of an active 14-year-old boy is:

- 13 MJ (pronounced as ‘13 megajoules’)
- 13 x 10
^{6}J - 1.3 x 10
^{7}J - 13 000 000 joules

#### Nature of Science

A large number of scientific terms have their origins in Latin words. The reason for this is that Latin was used in scholarly writing well into the 19th century. For example, Sir Isaac Newton’s major works, such as *Principia*, were all written in Latin. Today, although the popularity of the language has fallen away, Latin roots continue to serve as a major source for the derivation of new terms in the sciences.

#### Useful links

A pictorial view of powers of 10.

http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

Cell size and scale.

http://learn.genetics.utah.edu/content/begin/cells/scale

Scale of the universe.

http://apod.nasa.gov/apod/ap140112.html