## Metric Prefixes

SI units are part of the **metric system**. The metric system is convenient for scientific and engineering calculations because the units are categorized by factors of 10. The table below gives metric prefixes and symbols used to denote various factors of 10.

Metric systems have the advantage that conversions of units involve only powers of 10. There are 100 centimeters in a meter, 1000 meters in a kilometer, and so on. In nonmetric systems, such as the system of U.S. customary units, the relationships are not as simple—there are 12 inches in a foot, 5280 feet in a mile, and so on.

Another advantage of the metric system is that the same unit can be used over extremely large ranges of values simply by using an appropriate metric prefix. For example, distances in meters are suitable in construction, while distances in kilometers are appropriate for air travel, and the tiny measure of nanometers are convenient in optical design. With the metric system there is no need to invent new units for particular applications.

Prefix | Symbol | Value | Example (some are approximate) | |||
---|---|---|---|---|---|---|

exa | E | \(10^{18}\) | exameter | Em | \(10^{18} \mathrm{m}\) | distance light travels in a century |

peta | P | \(10^{15}\) | petasecond | Ps | \(10^{15} \mathrm{s}\) | 30 million years |

tera | T | \(10^{12}\) | terawatt | TW | \(10^{12} \mathrm{W}\) | powerful laser output |

giga | G | \(10^{9}\) | gigahertz | GHz | \(10^{9} \mathrm{Hz}\) | a microwave frequency |

mega | M | \(10^{6}\) | megacurie | MCi | \(10^{6} \mathrm{Ci}\) | high radioactivity |

kilo | k | \(10^{3}\) | kilometer | km | \(10^{3} \mathrm{m}\) | about 6/10 mile |

hecto | h | \(10^{2}\) | hectoliter | hL | \(10^{2} \mathrm{L}\) | 26 gallons |

deka | da | \(10^{1}\) | dekagram | dag | \(10^{1} \mathrm{g}\) | teaspoon of butter |

— | — | \(10^{0} (= 1)\) | ||||

deci | d | \(10^{-1}\) | deciliter | dL | \(10^{-1} \mathrm{L}\) | less than half a soda |

centi | c | \(10^{-2}\) | centimeter | cm | \(10^{-2} \mathrm{m}\) | fingertip thickness |

milli | m | \(10^{-3}\) | millimeter | mm | \(10^{-3} \mathrm{m}\) | flea at its shoulders |

micro | µ | \(10^{-6}\) | micrometer | µm | \(10^{-6} \mathrm{m}\) | detail in microscope |

nano | n | \(10^{-9}\) | nanogram | ng | \(10^{-9} \mathrm{g}\) | small speck of dust |

pico | p | \(10^{-12}\) | picofarad | pF | \(10^{-12} \mathrm{F}\) | small capacitor in radio |

femto | f | \(10^{-15}\) | femtometer | fm | \(10^{-15} \mathrm{m}\) | size of a proton |

atto | a | \(10^{-18}\) | attosecond | as | \(10^{-18} \mathrm{s}\) | time light crosses an atom |

### Order of Magnitude

The term order of magnitude refers to the scale of a value expressed in the metric system. Each power of \(10\) in the metric system represents a different order of magnitude. For example, \(10^{1}, 10^{2}, 10^{3},\) and so forth are all different orders of magnitude. All quantities that can be expressed as a product of a specific power of \(10\) are said to be of the *same* order of magnitude. For example, the number \(800\) can be written as \(8 × 10^2\), and the number 450 can be written as \(4.5 × 10^2\). Thus, the numbers \(800\) and \(450\) are of the same order of magnitude: \(10^2\). Order of magnitude can be thought of as a ballpark estimate for the scale of a value. The diameter of an atom is on the order of \(10^{-9} \mathrm{m},\) while the diameter of the Sun is on the order of \(10^9 \mathrm{m}.\)

## The Quest for Microscopic Standards for Basic Units

The fundamental units you have seen are those that produce the greatest accuracy and precision in measurement. There is a sense among physicists that, because there is an underlying microscopic substructure to matter, it would be most satisfying to base our standards of measurement on microscopic objects and fundamental physical phenomena such as the speed of light. A microscopic standard has been accomplished for the standard of time, which is based on the oscillations of the cesium atom.

The standard for length was once based on the wavelength of light (a small-scale length) emitted by a certain type of atom, but it has been supplanted by the more precise measurement of the speed of light. If it becomes possible to measure the mass of atoms or a particular arrangement of atoms such as a silicon sphere to greater precision than the kilogram standard, it may become possible to base mass measurements on the small scale.

There are also possibilities that electrical phenomena on the small scale may someday allow us to base a unit of charge on the charge of electrons and protons, but at present current and charge are related to large-scale currents and forces between wires.