Metric prefix

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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.

Contents

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 standardised for use in the International System of Units (SI) by the International Bureau of Weights and Measures (BIPM) in resolutions dating from 1960 to 2022. [1] [2] Since 2009, they have formed part of the ISO/IEC 80000 standard. They are also used in the Unified Code for Units of Measure (UCUM).

List of SI prefixes

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

PrefixBase 10 Decimal Adoption
[nb 1]
NameSymbol
quettaQ 1030 10000000000000000000000000000002022
ronnaR 1027 10000000000000000000000000002022
yottaY 1024 10000000000000000000000001991
zettaZ 1021 10000000000000000000001991
exaE 1018 10000000000000000001975
petaP 1015 10000000000000001975
teraT 1012 10000000000001960
giga G 109 10000000001960
mega M 106 10000001873
kilo k 103 10001795
hecto h 102 1001795
deca da 101 101795
100 1
deci d 10−1 0.11795
centi c 10−2 0.011795
milli m 10−3 0.0011795
micro μ 10−6 0.0000011873
nano n 10−9 0.0000000011960
picop 10−12 0.0000000000011960
femtof 10−15 0.0000000000000011964
attoa 10−18 0.0000000000000000011964
zeptoz 10−21 0.0000000000000000000011991
yoctoy 10−24 0.0000000000000000000000011991
rontor 10−27 0.0000000000000000000000000012022
quectoq 10−30 0.0000000000000000000000000000012022
Notes
  1. Prefixes adopted before 1960 already existed before SI. The introduction of the CGS system was in 1873.

First uses of prefixes in SI date back to definition of kilogram after the French Revolution at the end of the 18th century. Several more prefixes came into use by the 1947 IUPAC 14th International Conference of Chemistry [3] before being officially adopted for the first time in 1960. [4]

The most recent prefixes adopted were ronna-, quetta-, ronto-, and quecto- in 2022, after a proposal from British metrologist Richard J. C. Brown. The large prefixes ronna- and quetta- were adopted in anticipation of needs from data science, and because unofficial prefixes that did not meet SI requirements were already circulating. The small prefixes were added as well even without such a driver in order to maintain symmetry. [5]

Rules

Usage

Examples

Examples of powers of units with metric prefixes

Examples with prefixes and powers

Micro symbol

When mega and micro were adopted in 1873, there were then three prefaces starting with "m", so it was necessary to use some other symbol besides upper and lowercase 'm'. Eventually the Greek letter "µ" was adopted.

However various other abbreviations remained common, including "mic", "mm", and "u", in part motivated by the lack of a "µ" key on most typewriters.

From about 1960 onwards, "u" prevailed in type-written documents. [10] Because ASCII, EBCDIC, and other common encodings lacked code-points for "µ", this tradition remained even as computers replaced typewriters.

When ISO 8859-1 was created, it included the "µ" symbol for micro at codepoint U+00b5.

The whole of ISO 8859-1 was incorporated into the initial version of Unicode, but subsequently Unicode version 6 deprecated the micro symbol on codepoint U+00b5 in favour of the Greek letter "μ" on codepoint U+03bc.

However it remains widely implemented due to its prevalence in older documents, especially on POSIX systems where UTF-8 has historically been well tolerated by utilities that previously handled ASCII.

Keyboard entry

Most keyboards do not have a "µ" key, so it is necessary to use a key-chord; this varies depending on the operating system, physical keyboard layout, and user's language.

For all keyboard layouts
  • On Microsoft Windows systems,
    • arbitrary Unicode codepoints can be entered in hexadecimal as: Alt+0181; note that a leading "0" is required, or
    • in the tradition of MS-DOS, IBM code page 437 code-points can be entered in decimal: Alt+230
      (this is recorded as the corresponding Unicode code-point);
  • On Linux systems,
    • arbitrary Unicode codepoints can be entered in hexadecimal as: Ctrl+⇧ Shift+u b5space, or
For QWERTY keyboard layouts
  • On Linux systems,
    • code-point U+00b5 can be entered as right-alt+m (provided the right alt key is configured to act as AltGr).
  • On MacOS systems, code-point U+00b5 can be entered as either ⌥ Opt+m or ⌥ Opt+Y.

Typesetting in Latex

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". [11]

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.[ citation needed ] The prefixes, including those introduced after 1960, are used with any metric unit, whether officially included in the SI or not (e.g., millidyne and milligauss). Metric prefixes may also be used with some non-metric units, but not, for example, with the non-SI units of time. [12]

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. The megagram does not share the risk of confusion that the tonne has with other units with the name "ton".[ citation needed ]

The kilogram is the only coherent unit of the International System of Units that includes a metric prefix. [13] :144

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, often use the hectolitre (100 litres).[ citation needed ]

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.[ citation needed ]

Length

The kilometre, metre, centimetre, millimetre, and smaller units are common. The decimetre is rarely used. The micrometre is often referred to by the older non-SI name micron . In some fields, such as chemistry, the ångström (0.1 nm) has been used commonly 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.[ citation needed ]

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 standardised to 86400 seconds so as not to create issues with the irregular leap second.[ citation needed ]

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 standardised variant of the year, equal to exactly 31557600 seconds (365+14 days). 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.[ citation needed ]

Angle

The SI unit of angle is the radian, but degrees, as well as arc-minutes and arc-seconds, see some scientific use.[ citation needed ]

Temperature

Common practice does not typically use the flexibility allowed by official policy in the case of the degree Celsius (°C). NIST states: [14] "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).[ citation needed ]

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).[ citation needed ]

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 capitalised and without a prefix (i.e. Cal) when referring to "dietary calories" in food. [15] 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 specialised units used in particular fields (e.g., megaelectronvolt, gigaparsec, millibarn, kilodalton). In astronomy, geology, and palaeontology, the year, with symbol a (from the Latin annus), is commonly used with metric prefixes: ka, Ma, and Ga. [16]

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), [14] 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." [17]

Non-standard prefixes

Distance marker on the Rhine at Rudesheim: 36 (XXXVI) myriametres from Basel. The stated distance is 360 km; the decimal mark in Germany is a comma. Myriameterstein36RudesheimRhein.JPG
Distance marker on the Rhine at Rüdesheim: 36 (XXXVI) myriametres from Basel. The stated distance is 360 km; the decimal mark in Germany is a comma.

Obsolete metric prefixes

Some of the prefixes formerly used in the metric system have fallen into disuse and were not adopted into the SI. [18] [19] [20] The decimal prefix for ten thousand, myria- (sometimes spelled myrio- ), and the early binary prefixes double- (2×) and demi- (1/2×) were parts of the original metric system adopted by France in 1795, [21] 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- (107) 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), kilomegatonnes (now gigatonnes), hectokilometres (now 100 kilometres) and the derived adjective hectokilometric (typically used for qualifying the fuel consumption measures). [22] These are not compatible with the SI.

Other obsolete double prefixes included "decimilli-" (10−4), which was contracted to "dimi-" [23] and standardised in France up to 1961.

There are no more letters of the Latin alphabet available for new prefixes (all the unused letters are already used for units). As such, Richard J. C. Brown (who proposed the prefixes adopted for 10±27 and 10±30) has proposed a reintroduction of compound prefixes (e.g. kiloquetta- for 1033) if a driver for prefixes at such scales ever materialises, with a restriction that the last prefix must always be quetta- or quecto-. This usage is not currently approved by the BIPM. [24] [25]

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 (109) and trillion (1012), respectively, for large quantities, typically currency [26] and population. [27]

The medical and automotive fields in the United States use the abbreviations cc or ccm for cubic centimetres. One  cubic centimetre is equal to one  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, [28] 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. [29]

Binary prefixes

Prefixes for multiples of
bits (bit) or bytes (B)
Decimal
Value SI
1000103k kilo
10002106M mega
10003109G giga
100041012T tera
100051015P peta
100061018E exa
100071021Z zetta
100081024Y yotta
100091027R ronna
1000101030Q quetta
Binary
Value IEC JEDEC
1024210Ki kibi Kkilo
10242220Mi mebi Mmega
10243230Gi gibi Ggiga
10244240Ti tebi T tera
10245250Pi pebi
10246260Ei exbi
10247270Zi zebi
10248280Yi yobi

The original metric system adopted by France in 1795 included the two binary prefixes double- (2×) and demi- (1/2×). [21] However, they were not retained when the SI prefixes were internationally adopted by the 11th CGPM conference in 1960.

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). The SI does not permit the metric prefixes to be used in this conflicting sense. [30] This practice was once sanctioned by some industry associations, including JEDEC. The International Electrotechnical Commission (IEC) standardised the system of binary prefixes (kibi-, mebi-, gibi-, etc.) for this purpose. [31] [lower-alpha 2]

See also

Footnotes

  1. me = 9.1093837015(28)×10−31 kg [9]
  2. The names and symbols of the binary prefixes standardised by the IEC include:
    • kibi (Ki) = 210 = 1024,
    • mebi (Mi) = 220 = 10242 = 1048576,
    • gibi (Gi) = 230 = 10243 = 1073741824,
    etc.

Related Research Articles

<span class="mw-page-title-main">Kilogram</span> Metric unit of mass

The kilogram is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially. It means 'one thousand grams'.

Kilo is a decimal unit prefix in the metric system denoting multiplication by one thousand (103). It is used in the International System of Units, where it has the symbol k, in lowercase.

<span class="mw-page-title-main">Litre</span> Unit of volume

The litre or liter is a metric unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metre (m3). A cubic decimetre occupies a volume of 10 cm × 10 cm × 10 cm and is thus equal to one-thousandth of a cubic metre.

Mega is a unit prefix in metric systems of units denoting a factor of one million (106 or 1000000). It has the unit symbol M. It was confirmed for use in the International System of Units (SI) in 1960. Mega comes from Ancient Greek: μέγας, romanized: mégas, lit. 'great'.

The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and based on the metre as the unit of length and either the kilogram as the unit of mass or the kilogram-force as the unit of force.</ref> and the world's most widely used system of measurement. Established and maintained by the General Conference on Weights and Measures (CGPM), it is the only system of measurement with an official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce.

<span class="mw-page-title-main">SI base unit</span> One of the seven units of measurement that define the Metric System

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<span class="mw-page-title-main">Tonne</span> Metric unit of mass equivalent to 1000 kilograms or 1 megagram

The tonne is a unit of mass equal to 1000 kilograms. It is a non-SI unit accepted for use with SI. It is also referred to as a metric ton to distinguish it from the non-metric units of the short ton, and the long ton. It is equivalent to approximately 2204.6 pounds, 1.102 short tons, and 0.984 long tons. The official SI unit is the megagram, a less common way to express the same mass.

<span class="mw-page-title-main">Metric system</span> Metre-based systems of measurement

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<span class="mw-page-title-main">Pascal (unit)</span> SI derived unit of pressure

The pascal is the unit of pressure in the International System of Units (SI), and is also used to quantify internal pressure, stress, Young's modulus, and ultimate tensile strength. The unit, named after Blaise Pascal, is defined as one newton per square metre and is equivalent to 10 barye (Ba) in the CGS system. The unit of measurement called standard atmosphere (atm) is defined as 101,325 Pa.

<span class="mw-page-title-main">Square metre</span> SI-derived unit of area

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A unit prefix is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units. Units of various sizes are commonly formed by the use of such prefixes. The prefixes of the metric system, such as kilo and milli, represent multiplication by powers of ten. In information technology it is common to use binary prefixes, which are based on powers of two. Historically, many prefixes have been used or proposed by various sources, but only a narrow set has been recognised by standards organisations.

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<span class="mw-page-title-main">History of the metric system</span> History of the metric system measurement standards

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