Metric prefix
A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any 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.^{[1]} 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 10 | Decimal | English word | Adoption^{[nb 1]} | Etymology | |||
---|---|---|---|---|---|---|---|---|
Name | Symbol | Short scale | Long scale | Language | Derived word | |||
yotta | Y | 10^{24} | 1000000000000000000000000 | septillion | quadrillion | 1991 | Greek | eight^{[nb 2]} |
zetta | Z | 10^{21} | 1000000000000000000000 | sextillion | trilliard | 1991 | Latin | seven^{[nb 2]} |
exa | E | 10^{18} | 1000000000000000000 | quintillion | trillion | 1975 | Greek | six |
peta | P | 10^{15} | 1000000000000000 | quadrillion | billiard | 1975 | Greek | five^{[nb 2]} |
tera | T | 10^{12} | 1000000000000 | trillion | billion | 1960 | Greek | four^{[nb 2]}, monster |
giga | G | 10^{9} | 1000000000 | billion | milliard | 1960 | Greek | giant |
mega | M | 10^{6} | 1000000 | million | 1873 | Greek | great | |
kilo | k | 10^{3} | 1000 | thousand | 1795 | Greek | thousand | |
hecto | h | 10^{2} | 100 | hundred | 1795 | Greek | hundred | |
deca | da | 10^{1} | 10 | ten | 1795 | Greek | ten | |
10^{0} | 1 | one | – | |||||
deci | d | 10^{−1} | 0.1 | tenth | 1795 | Latin | ten | |
centi | c | 10^{−2} | 0.01 | hundredth | 1795 | Latin | hundred | |
milli | m | 10^{−3} | 0.001 | thousandth | 1795 | Latin | thousand | |
micro | μ | 10^{−6} | 0.000001 | millionth | 1873 | Greek | small | |
nano | n | 10^{−9} | 0.000000001 | billionth | milliardth | 1960 | Greek | dwarf |
pico | p | 10^{−12} | 0.000000000001 | trillionth | billionth | 1960 | Spanish | peak, beak, little bit |
femto | f | 10^{−15} | 0.000000000000001 | quadrillionth | billiardth | 1964 | Danish | fifteen |
atto | a | 10^{−18} | 0.000000000000000001 | quintillionth | trillionth | 1964 | Danish | eighteen |
zepto | z | 10^{−21} | 0.000000000000000000001 | sextillionth | trilliardth | 1991 | Latin | seven^{[nb 2]} |
yocto | y | 10^{−24} | 0.000000000000000000000001 | septillionth | quadrillionth | 1991 | Greek | eight^{[nb 2]} |
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. Except for the early prefixes of kilo-, hecto-, and deca-, the symbols for the multiplicative prefixes are uppercase letters, and those for the fractional prefixes are lowercase letters.^{[2]} There is a Unicode symbol for micro µ for use if the Greek letter μ is unavailable.^{[Note 1]} When both are unavailable, the visually similar lowercase Latin letter u is commonly used instead. SI unit symbols are never italicised.
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 deci-, and centi-, and less frequently hecto- and deca-, are commonly used for everyday purposes, and the centimetre (cm) is especially common. 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".^{[3]}
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 multiplicative prefix must be considered part of the unit, and thus included in the exponentiation:
- 1 km^{2} means one square kilometre, or the area of a square of 1000 m by 1000 m and not 1000 square metres.
- 2 Mm^{3} means two cubic megametres, or the volume of two cubes of 1000000 m by 1000000 m by 1000000 m or 2×10^{18} m^{3}, and not 2000000 cubic metres (2×10^{6} m^{3}).
- Examples
- 5 cm = 5×10^{−2} m = 5 × 0.01 m = 0.05 m.
- 9 km^{2} = 9 × (10^{3} m)^{2} = 9 × (10^{3})^{2} × m^{2} = 9×10^{6} m^{2} = 9 × 1000000 m^{2} = 9000000 m^{2}.
- 3 MW = 3×10^{6} 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".^{[citation needed]}
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 liquids, and the decilitre is used less frequently. Bulk agricultural products, such as grain, beer and wine, are often measured in hectolitres (each 100 litres in size).
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 still referred to by the older non-SI term micron. In some fields, such as chemistry, the ångström (equal to 0.1 nm) was historically used instead of 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, ad hoc non-metric units are used, such as the solar radius, 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 31557600 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, and seconds see some scientific use.
Temperature
Official policy also varies from common practice for the degree Celsius (°C). NIST states:^{[4]} "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.^{[5]} 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 metric SI system. 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). 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.^{[citation needed]} In astronomy, 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),^{[4]} 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."^{[6]}
An advantage of the SI system decimal prefixes is that they make for simplicity of calculation and conversion involving units of different sizes; consider for example the simplicity of buying 13 items of 390 g weight at €12.34 per kilogram, compared with items of 13+3⁄4 oz at $4.79 per pound (or, worse, with old non-metric currency: £4/15/9½). In the units used in the US, combining of units that are not decimal multiples of each other is often avoided by not mixing the units used, e.g., using inches, feet or miles only: 89 inches rather than 7 feet 5 inches (or 2 yards, 1 foot 5 inches).
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.^{[citation needed]} 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.^{[7]}^{[citation needed]}
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.^{[8]}^{[9]}^{[10]} The decimal prefix for ten thousand, myria- (sometimes also written as myrio-), and the binary prefixes double- (2×) and demi- (1/2×) were parts of the original metric system adopted by France in 1795,^{[11]} but were not retained when the SI prefixes were internationally adopted by the 11th CGPM conference in 1960.
Other metric prefixes used historically include hebdo- (10^{7}) and micri- (10^{−14}).
Double prefixes
Double prefixes have been used in the past, such as micromillimetres or millimicrons (now nanometres), micromicrofarads (μμF; now picofarads, pF), 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.
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".
The financial and general news media mostly use m or M, b or B, and t or T as abbreviations for million, billion (10^{9}) and trillion (10^{12}), respectively, for large quantities, typically currency^{[14]} and population.^{[15]}
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, engineers used the abbreviation MCM to designate a "thousand circular mils" in specifying the cross-sectional area 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,^{[16]} 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 1000.^{[17]}
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.^{[18]}^{[Note 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
- Orders of magnitude (data)
- RKM code
- SI base unit
- Unified Code for Units of Measure
Notes
- ^ On Microsoft Windows systems, Alt+230 will yield the symbol for micro µ. With macOS systems it is ⌥ Opt+Y or ⌥ Opt+m, and with Linux systems it is Ctrl+⇧ Shift+u b5space.
- ^ The names and symbols of the binary prefixes proposed by the IEC include etc.
References
- ^ "Four Resolutions". Bipm.org. Retrieved 2012-03-01.
- ^ "Metric Prefixes and SI Units". learn.sparkfun.com. Retrieved 2020-01-26.
- ^ Public Buildings Service, U.S. General Services Administration (September 1995). "METRIC DESIGN GUIDE (PBS-PQ260)" (PDF). National Institute of Building Sciences. Archived from the original (PDF) on 2011-12-15. Retrieved 2018-04-21.
- ^ ^{a} ^{b} Thompson, Ambler; Taylor, Barry N. (March 2008), "Special Publication 811", NIST (2008 ed.), retrieved 2018-06-21
- ^ Conn, Carole; Len Kravitz. "Remarkable Calorie". University of New Mexico. Retrieved 2017-05-22.
- ^ "SI Brochure: The International System of Units (SI)". International Bureau of Weights and Measures. Retrieved 2017-03-05.
- ^ isabel.chavez@nist.gov (2010-01-13). "Metric (SI) Prefixes". NIST. Retrieved 2021-04-09.
- ^ 29th Congress of the United States, Session 1 (1866-05-13). "H.R. 596, An Act to authorize the use of the metric system of weights and measures". Archived from the original on 2015-07-05.
- ^ Brewster, David (1830). The Edinburgh Encyclopædia. 12. Edinburgh, UK: William Blackwood, John Waugh, John Murray, Baldwin & Cradock, J. M. Richardson. p. 494. Retrieved 2015-10-09.
- ^ Brewster, David (1832). The Edinburgh Encyclopaedia. 12 (1st American ed.). Joseph and Edward Parker. Retrieved 2015-10-09.
- ^ "(section) La Loi Du 18 Germinal An 3" (in French). histoire.du.metre.free.fr. Retrieved 2015-10-12.
- ^ Rowlett, Russ (2008) [2000]. "millimicro-". 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.
- ^ Danloux-Dumesnils, Maurice (1969). 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 système métrique, 1965)
- ^ The Associated Press (2012-02-13). "Obama unveils $3.8T budget proposal". Cbc.ca. Retrieved 2012-03-01.
- ^ "More than 65M Flock to Discovery's Planet Earth". Multichannel.com. Retrieved 2012-03-01.
- ^ "Purcell, P (2007). Disambiguating M. PESA News 88". Pesa.com.au. Retrieved 2012-03-01.
- ^ "What is the difference between MCM and kcmil?". Reference.com. Retrieved 2016-09-05.
- ^ International Electrotechnical Commission (January 2010). "IEC 60050 - International Electrotechnical Vocabulary - Details for IEV number 112-01-27". Retrieved 2011-06-19.