# Metric prefix

# Metric prefix

A **metric prefix** is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. While all metric prefixes in common use today are decadic, historically there have been a number of binary metric prefixes as well.^{[3]} Each prefix has a unique symbol that is prepended to the unit symbol. The prefix *kilo-*, for example, may be added to *gram* to indicate *multiplication* by one thousand: one kilogram is equal to one thousand grams. The prefix *milli-*, likewise, may be added to *metre* to indicate *division* by one thousand; one millimetre is equal to one thousandth of a metre.

Decimal multiplicative prefixes have been a feature of all forms of the metric system, with six of these dating back to the system's introduction in the 1790s. Metric prefixes have also been used with some non-metric units. The **SI prefixes** are metric prefixes that were standardized for use in the International System of Units (SI) by the International Bureau of Weights and Measures (BIPM) in resolutions dating from 1960 to 1991.^{[4]} Since 2009, they have formed part of the International System of Quantities. They are also used in the Unified Code for Units of Measure (UCUM)

List of SI prefixes

The BIPM specifies twenty prefixes for the International System of Units (SI).

Prefix | Base 1000 | Base 10 | Decimal | English word | Adoption^{[1]} | ||
---|---|---|---|---|---|---|---|

Name | Symbol | Short scale | Long scale | ||||

yotta | Y | 1000^{8} | 1024 | 1000000000000000000000000 | septillion | quadrillion | 1991 |

zetta | Z | 1000^{7} | 1021 | 1000000000000000000000 | sextillion | trilliard | 1991 |

exa | E | 1000^{6} | 1018 | 1000000000000000000 | quintillion | trillion | 1975 |

peta | P | 1000^{5} | 1015 | 1000000000000000 | quadrillion | billiard | 1975 |

tera | T | 1000^{4} | 1012 | 1000000000000 | trillion | billion | 1960 |

giga | G | 1000^{3} | 109 | 1000000000 | billion | milliard | 1960 |

mega | M | 1000^{2} | 106 | 1000000 | million | 1873 | |

kilo | k | 1000^{1} | 103 | 1000 | thousand | 1795 | |

hecto | h | 1000^{2/3} | 102 | 100 | hundred | 1795 | |

deca | da | 1000^{1/3} | 101 | 10 | ten | 1795 | |

1000^{0} | 100 | 1 | one | – | |||

deci | d | 1000^{−1/3} | 10−1 | 0.1 | tenth | 1795 | |

centi | c | 1000^{−2/3} | 10−2 | 0.01 | hundredth | 1795 | |

milli | m | 1000^{−1} | 10−3 | 0.001 | thousandth | 1795 | |

micro | μ | 1000^{−2} | 10−6 | 0.000001 | millionth | 1873 | |

nano | n | 1000^{−3} | 10−9 | 0.000000001 | billionth | milliardth | 1960 |

pico | p | 1000^{−4} | 10−12 | 0.000000000001 | trillionth | billionth | 1960 |

femto | f | 1000^{−5} | 10−15 | 0.000000000000001 | quadrillionth | billiardth | 1964 |

atto | a | 1000^{−6} | 10−18 | 0.000000000000000001 | quintillionth | trillionth | 1964 |

zepto | z | 1000^{−7} | 10−21 | 0.000000000000000000001 | sextillionth | trilliardth | 1991 |

yocto | y | 1000^{−8} | 10−24 | 0.000000000000000000000001 | septillionth | quadrillionth | 1991 |

Each prefix name has a symbol that is used in combination with the symbols for units of measure. For example, the symbol for 'kilo-' is 'k', and is used to produce 'km', 'kg', and 'kW', which are the SI symbols for kilometre, kilogram, and kilowatt, respectively. Where the Greek letter 'μ' is unavailable, the symbol for micro 'µ' may be used. Where both variants are unavailable, the micro prefix is commonly written as the lowercase Latin letter 'u'.

Prefixes corresponding to an integer power of one thousand are generally preferred. Hence '100 m' is preferred over '1 hm' (hectometre) or '10 dam' (decametres). The prefixes hecto, deca, deci, and centi are commonly used for everyday purposes, and the centimetre (cm) is especially common. However, some modern building codes require that the millimetre be used in preference to the centimetre, because "use of centimetres leads to extensive usage of decimal points and confusion".^{[5]}

Prefixes may not be used in combination. This also applies to mass, for which the SI base unit (kilogram) already contains a prefix. For example, milligram (mg) is used instead of microkilogram (μkg).

In the arithmetic of measurements having units, the units are treated as multiplicative factors to values. If they have prefixes, all but one of the prefixes must be expanded to their numeric multiplier, except when combining values with identical units. Hence,

5 mV × 5 mA = 5×10−3 V × 5×10−3 A = 25×10−6 V⋅A = 25 μW

5.00 mV + 10 μV = 5.00 mV + 0.01 mV = 5.01 mV

When powers of units occur, for example, squared or cubed, the multiplication prefix must be considered part of the unit, and thus included in the exponentiation.

- Examples

5 cm = 5×10−2 m = 5 × 0.01 m = 0.05 m

9 km2 = 9 × (103 m)2 = 9 × (103)2 × m2 = 9×106 m2 = 9 × 1000000 m2 = 9000000 m2

3 MW = 3×106 W = 3 × 1000000 W = 3000000 W

Application to units of measurement

The use of prefixes can be traced back to the introduction of the metric system in the 1790s, long before the 1960 introduction of the SI. The prefixes, including those introduced after 1960, are used with any metric unit, whether officially included in the SI or not (e.g., millidynes and milligauss). Metric prefixes may also be used with non-metric units.

The choice of prefixes with a given unit is usually dictated by convenience of use. Unit prefixes for amounts that are much larger or smaller than those actually encountered are seldom used.

Metric units

Mass

The units kilogram, gram, milligram, microgram, and smaller are commonly used for measurement of mass. However, megagram, gigagram, and larger are rarely used; tonnes (and kilotonnes, megatonnes, etc.) or scientific notation are used instead. Megagram and teragram are occasionally used to disambiguate the metric tonne from other units with the name 'ton'.

The kilogram is the only base unit of the International System of Units that includes a metric prefix.

Volume

The litre (equal to a cubic decimetre), millilitre (equal to a cubic centimetre), microlitre, and smaller are common. In Europe, the centilitre is often used for packaged products such as wine and the decilitre is used less frequently.

Larger volumes are usually denoted in kilolitres, megalitres or gigalitres, or else in cubic metres (1 cubic metre = 1 kilolitre) or cubic kilometres (1 cubic kilometre = 1 teralitre). For scientific purposes, the cubic metre is usually used.

Length

The kilometre, metre, centimetre, millimetre, and smaller are common. (However, the decimetre is rarely used.) The micrometre is often referred to by the non-SI term *micron*. In some fields, such as chemistry, the ångström (equal to 0.1 nm) historically competed with the nanometre. The femtometre, used mainly in particle physics, is sometimes called a fermi. For large scales, megametre, gigametre, and larger are rarely used. Instead, non-metric units are used, such as astronomical units, light years, and parsecs; the astronomical unit is mentioned in the SI standards as an accepted non-SI unit.

Time

Prefixes for the SI standard unit second are most commonly encountered for quantities less than one second. For larger quantities, the system of minutes (60 seconds), hours (60 minutes) and days (24 hours) is accepted for use with the SI and more commonly used. When speaking of spans of time, the length of the day is usually standardized to 86400 seconds so as not to create issues with the irregular leap second.

Larger multiples of the second such as kiloseconds and megaseconds are occasionally encountered in scientific contexts, but are seldom used in common parlance. For long-scale scientific work, particularly in astronomy, the Julian year or *annum* is a standardized variant of the year, equal to exactly 31,557,600 SI seconds (365 days, 6 hours). The unit is so named because it was the average length of a year in the Julian calendar. Long time periods are then expressed by using metric prefixes with the annum, such as megaannum or gigaannum.

Angle

The SI unit of angle is the radian, but degrees, minutes, seconds and more rarely tierces see some scientific use.

Temperature

Official policy also varies from common practice for the degree Celsius (°C). NIST states:^{[6]} "Prefix symbols may be used with the unit symbol °C and prefix names may be used with the unit name 'degree Celsius'. For example, 12 m°C (12 millidegrees Celsius) is acceptable." In practice, it is more common for prefixes to be used with the kelvin when it is desirable to denote extremely large or small absolute temperatures or temperature differences. Thus, temperatures of star interiors may be given in units of MK (megakelvins), and molecular cooling may be described in mK (millikelvins).

Energy

In use the joule and kilojoule are common, with larger multiples seen in limited contexts. In addition, the kilowatt hour, a composite unit formed from the kilowatt and hour, is often used for electrical energy; other multiples can be formed by modifying the prefix of watt (e.g. terawatt hour).

There exist a number of definitions for the non-SI unit, the calorie. There are gram calories and kilogram calories. One kilogram calorie, which equals one thousand gram calories, often appears capitalized and without a prefix (i.e. 'Cal') when referring to "dietary calories" in food.^{[7]} It is common to apply metric prefixes to the gram calorie, but not to the kilogram calorie: thus, 1 kcal = 1000 cal = 1 Cal.

Non-metric units

Metric prefixes are widely used outside the system of metric units. Common examples include the megabyte and the decibel. Metric prefixes rarely appear with imperial or US units except in some special cases (e.g., microinch, kilofoot, kilopound or 'kip'). They are also used with other specialized units used in particular fields (e.g., megaelectronvolt, gigaparsec, millibarn). They are also occasionally used with currency units (e.g., gigadollar), mainly by people who are familiar with the prefixes from scientific usage. In geology and paleontology, the year, with symbol a (from the Latin *annus*), is commonly used with metric prefixes: ka, Ma, and Ga.

Official policies about the use of SI prefixes with non-SI units vary slightly between the International Bureau of Weights and Measures (BIPM) and the American National Institute of Standards and Technology (NIST). For instance, the NIST advises that "to avoid confusion, prefix symbols (and prefix names) are not used with the time-related unit symbols (names) min (minute), h (hour), d (day); nor with the angle-related symbols (names) ° (degree), ′ (minute), and ″ (second)",^{[6]} whereas the BIPM adds information about the use of prefixes with the symbol 'as' for arcsecond when they state: "However astronomers use milliarcsecond, which they denote mas, and microarcsecond, μas, which they use as units for measuring very small angles."^{[8]}

Presentation

Pronunciation

When a metric prefix is affixed to a root word, the prefix carries the stress, while the root drops its stress but retains a full vowel in the syllable that is stressed when the root word stands alone. For example, *kilobyte* is /ˈkɪlɒbaɪt/, with stress on the first syllable. However, units in common use outside the scientific community may be stressed idiosyncratically. In English-speaking countries, *kilometre* is the most conspicuous example. It is often pronounced /kɪˈlɒmɪtər/, with reduced vowels on both syllables of *metre*. This stress is not applied to other multiples or sub-multiples of metre, or to other units prefixed with 'kilo'.

The prefix *giga* is usually pronounced in English as /ˈɡɪɡə/, with hard ⟨g⟩ as in 'get', but sometimes /ˈdʒɪɡə/, with soft ⟨g⟩ as in 'gin'.

Typesetting

The LaTeX typesetting system features an *SIunitx* package in which the units of measurement are spelled out, for example, \SI{3}{\tera\hertz} formats as "3 THz".

Non-standard prefixes

Obsolete metric prefixes

Some of the prefixes formerly used in the metric system have fallen into disuse and were not adopted into the SI.^{[9]}^{[10]}^{[11]} The decimal prefix *myria-* (sometimes also written as *myrio-*) (ten thousand) as well as the binary prefixes *double-* and *demi-*, denoting a factor of 2 and 1/2 (one half), respectively, were parts of the original metric system adopted by France in 1795.^{[3]} These were not retained when the SI prefixes were internationally adopted by the 11th CGPM conference in 1960.

Other metric prefixes used historically include hebdo- (107) and micri- (10−14).

Double prefixes

Double prefixes have been used in the past, such as *micromillimetres* or "millimicrons" (now nanometres), *micromicrofarads* (now picofarads), *kilomegatons* (now gigatons), *hectokilometres* (now 100 kilometres) and the derived adjective *hectokilometric* (typically used for qualifying the fuel consumption measures).^{[12]} These are not compatible with the SI.

Other obsolete double prefixes included "decimilli-" (10−4), which was contracted to "dimi-"^{[13]} and standardized in France up to 1961.

Proposals for future prefixes

Although the *yotta-* prefix is large, the field of computer data is likely to approach values reaching or exceeding yottabytes in the future. Thus, various proposals for a prefix beyond *yotta-* have been put forth.

"Hella" prefix proposal

In 2010, UC Davis student Austin Sendek started a petition to designate "hella" as the SI prefix for one octillion (short scale; long scale: quadrilliard; 1027).^{[14]} The petition gathered over 60,000 supporters by circulating through Facebook and media coverage.^{[15]} It was also adopted by Wolfram Alpha.^{[16]}

R and Q

A proposal made to the BIPM is ronna (R) for 1027, quecca (Q) for 1030, ronto (r) for 10−27 and quecto (q) for 10−30.^{[17]}

Similar symbols and abbreviations

In written English, the symbol *K* is often used informally to indicate a multiple of thousand in many contexts. For example, one may talk of a *40K salary* (40000), or call the Year 2000 problem the *Y2K problem*. In these cases, an uppercase K is often used with an implied unit (although it could then be confused with the symbol for the kelvin temperature unit if the context is unclear). This informal postfix is read or spoken as "thousand" or "grand", or just "k", but never "kilo" (despite that being the origin of the letter).

The financial and general news media mostly use m/M, b/B and t/T as abbreviations for million, billion (109) and trillion (1012), respectively, for large quantities, typically currency^{[18]} and population.^{[19]}

The medical and automotive fields in the United States use the abbreviations "cc" or "ccm" for cubic centimetres. 1 cubic centimetre is equivalent to 1 millilitre.

For nearly a century, the electrical construction industry used the abbreviation "MCM" to designate a "thousand circular mils" in specifying thicknesses of large electrical cables. Since the mid-1990s, "kcmil" has been adopted as the "official" designation of a thousand circular mils, but the designation "MCM" still remains in wide use. A similar system is used in natural gas sales in the United States: m (or M) for thousands and mm (or MM) for millions of British thermal units or therms, and in the oil industry,^{[20]} where 'MMbbl' is the symbol for 'millions of barrels'. This usage of the capital letter M for 'thousand' is from Roman numerals, in which M means 1,000.^{[21]}

Binary prefixes

In some fields of information technology, it has been common to designate non-decimal multiples based on powers of 1024, rather than 1000, for some SI prefixes (kilo, mega, giga), contrary to the definitions in the International System of Units (SI). This practice was once sanctioned by some industry associations, including JEDEC. The International Electrotechnical Commission (IEC) standardized the system of binary prefixes (kibi, mebi, gibi, etc.) for this purpose.^{[22]}^{[2]}

See also

Engineering notation

E1 series (preferred numbers)

Indian numbering system

International vocabulary of metrology

ISO/IEC 80000

List of numbers in various languages (for comparison/etymology)

Names of large numbers

Names of small numbers

Number names

Numeral prefix

Order of magnitude

RKM code

SI base unit

Unified Code for Units of Measure

## References

*archive.org*. 2011-12-15. Retrieved 2018-04-21.

*NIST*(2008 ed.), retrieved 2018-06-21

*The Edinburgh Encyclopædia*.

**12**. Edinburgh, UK: William Blackwood, John Waugh, John Murray, Baldwin & Cradock, J. M. Richardson. p. 494. Retrieved 2015-10-09.

*The Edinburgh Encyclopaedia*.

**12**(1st American ed.). Joseph and Edward Parker. Retrieved 2015-10-09.

*How Many? A Dictionary of Units of Measurement*. University of North Carolina at Chapel Hill. Archived from the original on 2016-08-29. Retrieved 2016-08-29.

*The metric system: a critical study of its principles and practice*. The Athlone Press. p. 34. Retrieved 2015-10-09. (a translation of the French original

*Esprit et bon usage du systeme metrique*, 1965)

*Los Angeles Times*.

*Science*. doi:10.1126/science.aax0020.

*Disambiguating M*. PESA News 88". Pesa.com.au. Retrieved 2012-03-01.