SI prefix

SI prefix

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The International System of Units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

 (SI) specifies a set of unit prefixes known as SI prefixes or metric prefixes. An SI prefix is a name that precedes a basic unit of measure to indicate a decadic
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....

 multiple
Multiple (mathematics)
In mathematics, a multiple is the product of any quantity and an integer. In other words, for the quantities a and b, we say that b is a multiple of a if b = na for some integer n , which is called the multiplier or coefficient. If a is not zero, this is equivalent to saying that b/a is an integer...

 or fraction
Fraction (mathematics)
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, we specify how many parts of a certain size there are, for example, one-half, five-eighths and three-quarters.A common or "vulgar" fraction, such as 1/2, 5/8, 3/4, etc., consists...

 of the unit. Each prefix has a unique symbol that is prepended to the unit symbol. The SI prefixes are standardized by the International Bureau of Weights and Measures
International Bureau of Weights and Measures
The International Bureau of Weights and Measures , is an international standards organisation, one of three such organisations established to maintain the International System of Units under the terms of the Metre Convention...

 in resolutions dating from 1960 to 1991. Their usage is not limited to SI units and many of these date back to the introduction of the metric system in the 1790s.

SI prefixes are used to reduce the number of zeros shown in numerical quantities before or after a decimal point. For example, an electrical current of , or one-billionth (short scale) of an ampere, is written by using the SI-prefix nano as or .

List of SI prefixes


The International System of Units specifies twenty SI prefixes:

Examples

= = = = = =

General use of prefix names and symbols


Twenty SI prefixes are available to combine with units of measure. For example, the prefix kilo- denotes a multiple of one thousand, so 1 kilometre
Kilometre
The kilometre is a unit of length in the metric system, equal to one thousand metres and is therefore exactly equal to the distance travelled by light in free space in of a second...

 equals 1000 metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

s, 1 kilogram
Kilogram
The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...

 equals 1000 gram
Gram
The gram is a metric system unit of mass....

s, 1 kilowatt equals 1000 watt
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...

s, and so on. Each SI prefix name has an associated symbol which can be used in combination with the symbols for units of measure. Thus, the "kilo-" symbol, k, can be used to produce km, kg, and kW, (kilometre, kilogram, and kilowatt). SI prefixes are internationally recognized and also exist outside the SI (many of them long pre-date SI, going back to the original introduction of the metric system); prefixes may also be used in combination with non-SI units; for example: milligauss (mG), kilofoot (kft) and microinch (µin).

Prefixes may not be used in combination. This even applies for mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

, for which the SI base unit
SI base unit
The International System of Units defines seven units of measure as a basic set from which all other SI units are derived. These SI base units and their physical quantities are:* metre for length...

 (which is the kilogram, not the gram) already contains a prefix. So milligram (mg) is used instead of microkilogram (µkg), for example.

Prefixed values cannot be multiplied or divided together, and they have to be converted into non-prefixed standard form for such calculations. For example, 5 mV × 5 mA ≠ 25 mW. The correct calculation is: 5 mV × 5 mA = 5 × 10−3 V × 5 × 10−3 A = 25 x 10−6 W = 25 µW = 0.025 mW.

Prefixes corresponding to an exponent that is divisible by three are often recommended. Hence "100 m" rather than "1 hm" (hectometre) or "10 dam" (decametres). The "non-three" prefixes (hecto-, deca-, deci-, and centi-) are however more commonly used for everyday purposes than in science.

SI prefixes with symbols for time and angles


Official policies about the use of these prefixes vary slightly between the Bureau International des Poids et Mesures (BIPM) and the American National Institute of Standards and Technology
National Institute of Standards and Technology
The National Institute of Standards and Technology , known between 1901 and 1988 as the National Bureau of Standards , is a measurement standards laboratory, otherwise known as a National Metrological Institute , which is a non-regulatory agency of the United States Department of Commerce...

 (NIST); and some of the policies of both bodies are at variance with everyday practice. For instance, the NIST advises that "…to avoid confusion, prefix symbols (and prefixes) 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)." The BIPM’s position on the use of SI prefixes with units of time larger than the second is the same as that of the NIST but their position with regard to angles differs: they state "However astronomers use milliarcsecond, which they denote mas, and microarcsecond, µas, which they use as units for measuring very small angles."

SI prefixes for temperature in °C


Official policy also varies from common practice for the degree Celsius (°C). NIST states; "Prefix symbols may be used with the unit symbol °C and prefixes may be used with the unit name 'degree Celsius'. For example, 12 m°C (12 millidegrees Celsius) is acceptable."

Exponentiation of symbols


When units occur in exponentiation
Exponentiation
Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent n...

, for example, in square and cubic forms, any size prefix is considered part of the unit, and thus included in the exponentiation. means one square kilometre
Kilometre
The kilometre is a unit of length in the metric system, equal to one thousand metres and is therefore exactly equal to the distance travelled by light in free space in of a second...

 or the size of a square
Square (geometry)
In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...

 of 1000 m by 1000 m and not 1000 square metre
Square metre
The square metre or square meter is the SI derived unit of area, with symbol m2 . It is defined as the area of a square whose sides measure exactly one metre...

s. means two cubic megametre
Megametre
A megametre is a unit of length in the metric system, equal to one million metres, the SI base unit of length, hence to 1,000 km or approximately 621.37 miles....

 or the size of two cube
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...

s of by by or , and not .

Pronunciation


There are two accepted pronunciations for the prefix giga-: ˈ and ˈ. According to the American writer Kevin Self, in the 1920s a German committee member of the International Electrotechnical Commission
International Electrotechnical Commission
The International Electrotechnical Commission is a non-profit, non-governmental international standards organization that prepares and publishes International Standards for all electrical, electronic and related technologies – collectively known as "electrotechnology"...

 proposed giga- as a prefix for 109, drawing on a verse by the humorous poet Christian Morgenstern that appeared in the third (1908) edition of Galgenlieder (Gallows Songs). This suggests a hard German g was originally intended as the pronunciation. Self was unable to ascertain at what point the /dʒ/ (soft g) pronunciation became accepted, but as of 1995 current practice had returned to /ɡ/ (hard g).
When an SI prefix is affixed to a root word, the prefix carries the stress
Stress (linguistics)
In linguistics, stress is the relative emphasis that may be given to certain syllables in a word, or to certain words in a phrase or sentence. The term is also used for similar patterns of phonetic prominence inside syllables. The word accent is sometimes also used with this sense.The stress placed...

, 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, gigabyte
Gigabyte
The gigabyte is a multiple of the unit byte for digital information storage. The prefix giga means 109 in the International System of Units , therefore 1 gigabyte is...

is ˈ, with stress on the first syllable. However, words in common use outside the scientific community may follow idiosyncratic stress rules. Kilometre is commonly pronounced /kɨˈlɒmɨtər/, with reduced vowels on both syllables of metre.

Disallowed and obsolete prefixes



The prefix myria- 'ten thousand' denoting a factor of , originated from the Greek μύριοι (mýrioi) for ten thousand, and the prefixes demi and double, denoting a factors of 1/2 and 2, respectively, were parts of the original metric system
Metric system
The metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...

 adopted by France in 1795. These were not retained when the SI prefixes were internationally adopted by the 11th CGPM conference in 1960. The binary prefixes were dropped because they were neither decimal nor symmetrical.

Double prefixes such as those formerly used in micromicrofarads
Farad
The farad is the SI unit of capacitance. The unit is named after the English physicist Michael Faraday.- Definition :A farad is the charge in coulombs which a capacitor will accept for the potential across it to change 1 volt. A coulomb is 1 ampere second...

 (picofarads), hectokilometres (100 kilometres), and millimicrons or micromillimetres (both nanometres) were disallowed with the introduction of the SI.
The choice of commonly used prefixes with a given unit is usually dictated by convenience of use, unit prefixes that are much larger or smaller than encountered in practice, are seldom used, albeit valid combinations. In most contexts only a few, the most common, standard combination are established:
  • Mass: kilogram, hectogram, gram, milligram, microgram, and smaller are common. However, megagram or larger are rarely used; tonnes (and kilotonnes etc.) or scientific notation
    Scientific notation
    Scientific notation is a way of writing numbers that are too large or too small to be conveniently written in standard decimal notation. Scientific notation has a number of useful properties and is commonly used in calculators and by scientists, mathematicians, doctors, and engineers.In scientific...

     are used instead. Megagram is occasionally used to disambiguate the (metric) tonne from the various (non-metric) tons. An exception is emission rates, which are typically on the order of Tg/yr. Sometimes only one element is denoted for an emission, such as Tg C/yr or Tg N/yr, so that inter-comparisons of different compounds are easier.
  • Volume in litres: litre, decilitre, centilitre, millilitre, microlitre, and smaller are common. Larger volumes are sometimes denoted in hectolitres; otherwise in cubic metres or cubic kilometres. In Australia, large quantities of water are measured in kilolitres, megalitres and gigalitres.
  • Length: kilometre, metre, decimetre, centimetre, millimetre, and smaller are common. The micrometre is often referred to by the non-SI term micron
    Micrometre
    A micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...

    . In some fields such as chemistry
    Chemistry
    Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

    , the angstrom
    Ångström
    The angstrom or ångström, is a unit of length equal to 1/10,000,000,000 of a meter . Its symbol is the Swedish letter Å....

     (equal to 0.1 nm) competes with the nanometre. The femtometre
    Femtometre
    The femtometre is an SI unit of length equal to 10-15 metres. This distance can also be called fermi and was so named in honour of Enrico Fermi and is often encountered in nuclear physics as a characteristic of this scale...

    , used mainly in particle physics, is usually called a fermi. For large scales, megametre, gigametre, and larger are rarely used. Often used are astronomical unit
    Astronomical unit
    An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....

    s, light years, and parsec
    Parsec
    The parsec is a unit of length used in astronomy. It is about 3.26 light-years, or just under 31 trillion kilometres ....

    s; the astronomical unit is mentioned in the SI standards as an accepted non-SI unit.
  • Time: second, millisecond, microsecond, and shorter are common. The kilosecond and megasecond also have some use, though for these and longer times one usually uses either scientific notation or minutes, hours, and so on.

Non-SI units


The use of prefixes can be traced back to the introduction of the metric system
Metric system
The metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...

 in the 1790s, long before the SI was introduced in 1960. The prefixes, including those introduced after the introduction of the SI, are used with any metric units, whether officially included in the SI or not (e.g., millidynes).

SI prefixes rarely appear with imperial unit
Imperial unit
The system of imperial units or the imperial system is the system of units first defined in the British Weights and Measures Act of 1824, which was later refined and reduced. The system came into official use across the British Empire...

s or English unit
English unit
English units are the historical units of measurement used in England up to 1824, which evolved as a combination of the Anglo-Saxon and Roman systems of units...

s except in some special cases (e.g., microinches, kilofeet, kilopound or 'kip'). They are also used with other specialized units used in particular fields (e.g., megaelectronvolts, gigaparsecs). They are also occasionally used with currency units (e.g., gigadollar), mainly by people who are familiar with the prefixes from scientific usage.

Similar symbols in abbreviations


The symbol K is often used informally to mean a multiple of thousand in many contexts. For example, one may talk of a 40K salary (40 000), or call the Year 2000 problem
Year 2000 problem
The Year 2000 problem was a problem for both digital and non-digital documentation and data storage situations which resulted from the practice of abbreviating a four-digit year to two digits.In computer programs, the practice of representing the year with two...

 as Y2K problem. In these cases an uppercase K is often used, although the uppercase K is the official symbol of the kelvin
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

.

In other financial and business contexts, the letter M is often used to denote multiplication by 1000, in recognition of the Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

 term mille (meaning one thousand), also used in roman numerals
Roman numerals
The numeral system of ancient Rome, or Roman numerals, uses combinations of letters from the Latin alphabet to signify values. The numbers 1 to 10 can be expressed in Roman numerals as:...

. In these situations one million is often written as 1 MM. In other financial situations, one M can mean million, such as £2M or £2m which is equal to £2 000 000. Similar usage of M occurs in the term CPM (Cost per mille
Cost Per Mille
Cost per mille , also called cost ‰ and cost per thousand , is a commonly used measurement in advertising. Radio, television, newspaper, magazine, out-of-home advertising, and online advertising can be purchased on the basis of what it costs to show the ad to one thousand viewers...

) used in advertising.

For nearly a century, the electrical construction industry used the acronym "MCM" to designate a "thousand circular mils" in specifying thicknesses of large electrical cables. Since the mid-1990s, the term "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 Btus or Therms.

Units used in computing and telecommunications


The International System of Units does not define units of information, such as the storage size units bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...

 and byte
Byte
The byte is a unit of digital information in computing and telecommunications that most commonly consists of eight bits. Historically, a byte was the number of bits used to encode a single character of text in a computer and for this reason it is the basic addressable element in many computer...

. This has allowed ambiguities to emerge with respect to the symbols in use, as well as their usage and meaning in combination with the SI prefixes. The bit is often given the symbol bit or b, while byte is usually written as byte, B, and occasionally as b. Thus, kb/s often means kilobits per second, but may sometimes refer to kilobytes per second.

The National Institute of Standards and Technology in the United States has suggested the use of bit for bits and B for bytes. The use of 'b' for 'bytes' is ambiguous and should be strongly discouraged.

In non-standard use, K is often used as a symbol prefix to the units bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...

 and byte
Byte
The byte is a unit of digital information in computing and telecommunications that most commonly consists of eight bits. Historically, a byte was the number of bits used to encode a single character of text in a computer and for this reason it is the basic addressable element in many computer...

 to designate the binary prefix
Binary prefix
In computing, a binary prefix is a specifier or mnemonic that is prepended to the units of digital information, the bit and the byte, to indicate multiplication by a power of 2...

 kibi = 210 = 1024.

Binary prefixes



The prefixes kilo, mega, giga and greater are often used in combination with the storage size units bit and byte.

The binary multiple 210 = 1024 is close to the value 1000 of the prefix kilo, therefore computer professionals have historically used the unit kilobyte to refer to 1024 bytes of computer memory
Computer memory
In computing, memory refers to the physical devices used to store programs or data on a temporary or permanent basis for use in a computer or other digital electronic device. The term primary memory is used for the information in physical systems which are fast In computing, memory refers to the...

, in non-conformance with the SI definition of the prefix kilo. Likewise, 220 = , which is close to has been expressed with the mega prefix. This has led to some confusion, because megabyte is commonly used to refer to in the specifications of hard disk drive capacities and network transmission bit rate
Bit rate
In telecommunications and computing, bit rate is the number of bits that are conveyed or processed per unit of time....

s. Although it is common to size disk drives in MB or GB(106 or 109) and refer to capacity as "megabytes" or "gigabytes", this has led to a number of lawsuits from purchasers who were expecting 220 or 230 and considered themselves shortchanged by the seller. To protect themselves, some sellers actually write out the full term as "1,000,000" or "1,000,000,000".

To eliminate this ambiguity the International Electrotechnical Commission
International Electrotechnical Commission
The International Electrotechnical Commission is a non-profit, non-governmental international standards organization that prepares and publishes International Standards for all electrical, electronic and related technologies – collectively known as "electrotechnology"...

 (IEC) adopted new binary prefix
Binary prefix
In computing, a binary prefix is a specifier or mnemonic that is prepended to the units of digital information, the bit and the byte, to indicate multiplication by a power of 2...

es in 1998 (IEC 80000-13:2008
ISO/IEC 80000
International standard ISO 80000 or IEC 80000—depending on which of the two international standards bodies International Organization for Standardization and International Electrotechnical Commission is in charge of each respective part—is a style guide for the use of physical quantities and units...

 formerly subclauses 3.8 and 3.9 of IEC 60027-2:2005
IEC 60027
IEC 60027 is the International Electrotechnical Commission's standard on Letter symbols to be used in electrical technology...

). Each binary prefix is formed from the first syllable of the decimal prefix with the similar value, and the syllable 'bi' . The symbols are the decimal symbol, always capitalized, followed by the letter 'i'.

According to this standard one kilobyte
Kilobyte
The kilobyte is a multiple of the unit byte for digital information. Although the prefix kilo- means 1000, the term kilobyte and symbol KB have historically been used to refer to either 1024 bytes or 1000 bytes, dependent upon context, in the fields of computer science and information...

 (1 kB) is 103 or 1000 bytes, whereas one kibibyte
Kibibyte
The kibibyte is a multiple of the unit byte for quantities of digital information. The binary prefix kibi means 1024; therefore, 1 kibibyte is . The unit symbol for the kibibyte is KiB. The unit was established by the International Electrotechnical Commission in 1999 and has been accepted for use...

 (1 KiB) is 210 or 1024 bytes. Likewise mebi (Mi; 220 or ), gibi (Gi; 230 or ), tebi (Ti; 240), pebi (Pi; 250), exbi (Ei; 260), zebi (Zi; 270) and yobi (Yi; 280).

The use of these new binary prefixes is increasing, but is largely limited to technical literature and new computer software.

Related proposals


In 2010, an online petition sought to establish hella
Hella (word)
Hella is a word associated with Northern California used throughout the United States and Canada. It is a contraction of the phrase "hell of a" or "hell of a lot [of]"....

 as the SI prefix for 1027. The prefix, which has since appeared in the San Francisco Chronicle
San Francisco Chronicle
thumb|right|upright|The Chronicle Building following the [[1906 San Francisco earthquake|1906 earthquake]] and fireThe San Francisco Chronicle is a newspaper serving primarily the San Francisco Bay Area of the U.S. state of California, but distributed throughout Northern and Central California,...

, Daily Telegraph
The Daily Telegraph
The Daily Telegraph is a daily morning broadsheet newspaper distributed throughout the United Kingdom and internationally. The newspaper was founded by Arthur B...

, Wired
Wired (magazine)
Wired is a full-color monthly American magazine and on-line periodical, published since January 1993, that reports on how new and developing technology affects culture, the economy, and politics...

and some other scientific magazines, was recognized by Google
Google
Google Inc. is an American multinational public corporation invested in Internet search, cloud computing, and advertising technologies. Google hosts and develops a number of Internet-based services and products, and generates profit primarily from advertising through its AdWords program...

 in May 2010. Ian Mills, president of the Consultative Committee on Units, considers the chances of official adoption to be remote.

See also

  • International vocabulary of metrology
    International vocabulary of metrology
    The International vocabulary of metrology is an attempt to find a common language and terminology in metrology, e.g. the science of measurements, across different fields of science, legislature and commerce...

  • ISO/IEC 80000
    ISO/IEC 80000
    International standard ISO 80000 or IEC 80000—depending on which of the two international standards bodies International Organization for Standardization and International Electrotechnical Commission is in charge of each respective part—is a style guide for the use of physical quantities and units...

  • International System of Units
    International System of Units
    The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

  • SI base unit
    SI base unit
    The International System of Units defines seven units of measure as a basic set from which all other SI units are derived. These SI base units and their physical quantities are:* metre for length...

  • SI derived unit
    SI derived unit
    The International System of Units specifies a set of seven base units from which all other units of measurement are formed, by products of the powers of base units. These other units are called SI derived units, for example, the SI derived unit of area is square metre , and of density is...

  • Binary prefix
    Binary prefix
    In computing, a binary prefix is a specifier or mnemonic that is prepended to the units of digital information, the bit and the byte, to indicate multiplication by a power of 2...

  • Engineering notation
    Engineering notation
    Engineering notation is a version of scientific notation in which the powers of ten must be multiples of three...

  • Metric system
    Metric system
    The metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...

  • Non-SI unit prefixes
  • Number names
    Number names
    In linguistics, number names are specific words in a natural language that represent numbers.In writing, numerals are symbols also representing numbers...

  • Names of large numbers
    Names of large numbers
    This article lists and discusses the usage and derivation of names of large numbers, together with their possible extensions.The following table lists those names of large numbers which are found in many English dictionaries and thus have a special claim to being "real words"...

  • Names of small numbers
    Names of small numbers
    This article lists and discusses the usage and derivation of names of small numbers.-Table of names:The following table lists English language names of small numbers used in the long and short scales, along with the power of ten, engineering notation, and International System of Units symbols and...

  • List of numbers in various languages (for comparison/etymology)
  • Order of magnitude
    Order of magnitude
    An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...

  • Scientific notation
    Scientific notation
    Scientific notation is a way of writing numbers that are too large or too small to be conveniently written in standard decimal notation. Scientific notation has a number of useful properties and is commonly used in calculators and by scientists, mathematicians, doctors, and engineers.In scientific...

  • Number prefix

External links