The 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. It is the world's most widely used system of measurement, both in everyday commerce and in science (SI) specifies a set of unit prefixes An affix is a morpheme that is attached to a word stem to form a new word. Affixes may be derivational, like English -ness and pre-, or inflectional, like English plural -s and past tense -ed. They are bound morphemes by definition; prefixes and suffixes may be separable affixes. Affixation is, thus, the linguistic process speakers use to form new known as SI prefixes or metric prefixes. An SI prefix is a name that precedes a basic unit of measure to indicate a decimal The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations multiple In mathematics, a multiple is the product of any quantity and an integer. In other words, for the quantity a such as integer, real number, or complex number, b is a multiple of a if b = na for some integer n. The n is also called coefficient or multiplier. Additionally, if a is not zero, this is equivalent to saying that b / a is an integer with or fraction A fraction is a number that can represent part of a whole 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 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 (SI) under the terms of the Metre Convention (Convention du Mètre). The organisation is usually referred to by its French initialism, BIPM in resolutions dating from 1960 to 1991.[1] 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 0.000000001ampere, or one-billionth (short scale There are other numbering systems which are neither long nor short scale such as the Chinese numbering system, the Indian numbering system, the Japanese numbering system, and the Korean numbering system. Many countries, including most in continental Europe, use the long scale) of an ampere, is written by using the SI-prefix nano Nano- is a prefix in the metric system denoting a factor of 10−9 or 0.000000001. It is frequently encountered in science and electronics for prefixing units of time and length, such as 30 nanoseconds (symbol ns), 100 nanometres (nm) or in the case of electrical capacitance, 100 nanofarads (nF) as 1 nanoampere or 1 nA.
List of SI prefixes
The International System of Units specifies twenty SI prefixes:
SI prefixes
| Prefix |
Symbol |
1000m |
10n |
Decimal The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations |
Short scale There are other numbering systems which are neither long nor short scale such as the Chinese numbering system, the Indian numbering system, the Japanese numbering system, and the Korean numbering system. Many countries, including most in continental Europe, use the long scale |
Long scale There are other numbering systems which are neither long nor short scale such as the Chinese numbering system, the Indian numbering system, the Japanese numbering system, and the Korean numbering system. Many countries, including most in continental Europe, use the long scale |
Since[1] |
| yotta Yotta is the largest unit prefix in the International System of Units denoting a factor of 1024 or 1000000000000000000000000. It has the unit symbol Y |
Y |
10008 |
1024 This list compares various sizes of positive numbers, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the so called short scale which is used in English speaking countries, as well as a name in the long scale which is used in a series of countries that do not have English as their national |
1000000000000000000000000 |
Septillion |
Quadrillion |
1991 |
| zetta Zetta- is a prefix in the metric system denoting a factor of 1021 or 1000000000000000000000 |
Z |
10007 |
1021 This list compares various sizes of positive numbers, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the so called short scale which is used in English speaking countries, as well as a name in the long scale which is used in a series of countries that do not have English as their national |
1000000000000000000000 |
Sextillion |
Trilliard |
1991 |
| exa |
E |
10006 |
1018 This list compares various sizes of positive numbers, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the so called short scale which is used in English speaking countries, as well as a name in the long scale which is used in a series of countries that do not have English as their national |
1000000000000000000 |
Quintillion |
Trillion |
1975 |
| peta Adopted in 1975, it comes from the Greek πέντε, meaning five, because it is equal to 10005. It is based on the model of tera- , and so peta-, coming from penta-, omits the third letter, n |
P |
10005 |
1015 This list compares various sizes of positive numbers, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the so called short scale which is used in English speaking countries, as well as a name in the long scale which is used in a series of countries that do not have English as their national |
1000000000000000 |
Quadrillion |
Billiard |
1975 |
| tera Confirmed in 1960, it comes from the Greek τέρας, meaning monster. It also bears a resemblance to the Greek prefix τετρα meaning four; the coincidence of it signifying the fourth power of 1000 served as a model for the higher-order prefixes peta, exa, zetta and yotta, all of which are deliberately distorted forms of the Latin or Greek |
T |
10004 |
1012 This list compares various sizes of positive numbers, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the so called short scale which is used in English speaking countries, as well as a name in the long scale which is used in a series of countries that do not have English as their national |
1000000000000 |
Trillion |
Billion |
1960 |
| giga The Oxford English Dictionary reports the earliest written use of giga in this sense to be in the Reports of the IUPAC 14th Conference in 1947: "The following prefixes to abbreviations for the names of units should be used: G giga 109×" |
G |
10003 |
109 1,000,000,000 is the natural number following 999,999,999 and preceding 1,000,000,001 |
1000000000 |
Billion |
Milliard |
1960 |
| mega Mega- is an prefix in the metric system denoting a factor of million. Confirmed in 1960, it comes from the Greek μέγας, meaning great |
M |
10002 |
106 |
1000000 |
Million |
1960 |
| kilo The kilo prefix is derived from the Greek word χίλιοι , meaning thousand. It was originally adopted by Antoine Lavoisier and his group in 1795, and introduced into the metric system in France with its establishment in 1799. The General Conference on Weights and Measures was formed in 1875 |
k |
10001 |
103 1000 is the natural number following 999 and preceding 1001 |
1000 |
Thousand |
1795 |
| hecto Hecto or hecta is a prefix in the metric system denoting a factor of one hundred. Adopted in 1795, it comes from the Greek ἑκατόν hekaton, meaning hundred |
h |
10002⁄3 |
102 100 (Roman numeral C, for centum) is the natural number following 99 and preceding 101 |
100 |
Hundred |
1795 |
| deca Deca- or deka- is a prefix in the metric system, also a numerical prefix, denoting a factor of ten. The term is derived from the Greek δέκα meaning "ten" |
da |
10001⁄3 |
101 10 (pronounced /ˈtɛn/ ( listen)) is an even natural number following 9 and preceding 11 |
10 |
Ten |
1795 |
|
|
10000 |
100 1 is a number, numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement. For example, a line segment of "unit length" is a line segment of length 1 |
1 |
One |
|
| deci Deci is a prefix in the metric system denoting a factor of one tenth. Adopted in 1795, the prefix comes from the Latin decimus, meaning tenth. Its most frequent use is in the decibel, used to measure sound intensity (relative to a reference) and many other ratios |
d |
1000−1⁄3 |
10−1 This list compares various sizes of positive numbers, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the so called short scale which is used in English speaking countries, as well as a name in the long scale which is used in a series of countries that do not have English as their national |
0.1 |
Tenth |
1795 |
| centi |
c |
1000−2⁄3 |
10−2 This list compares various sizes of positive numbers, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the so called short scale which is used in English speaking countries, as well as a name in the long scale which is used in a series of countries that do not have English as their national |
0.01 |
Hundredth |
1795 |
| milli Milli is a prefix in the metric system denoting a factor of one thousandth. Adopted in 1795, the prefix comes from the Latin mille, meaning one thousand (the plural is milia) |
m |
1000−1 |
10−3 This list compares various sizes of positive numbers, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the so called short scale which is used in English speaking countries, as well as a name in the long scale which is used in a series of countries that do not have English as their national |
0.001 |
Thousandth |
1795 |
| micro Micro is a prefix in the metric system denoting a factor of one millionth. Confirmed in 1960, the prefix comes from the Greek μικρός (mikrós), meaning "small" |
μ |
1000−2 |
10−6 This list compares various sizes of positive numbers, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the so called short scale which is used in English speaking countries, as well as a name in the long scale which is used in a series of countries that do not have English as their national |
0.000001 |
Millionth |
1960[2] |
| nano Nano- is a prefix in the metric system denoting a factor of 10−9 or 0.000000001. It is frequently encountered in science and electronics for prefixing units of time and length, such as 30 nanoseconds (symbol ns), 100 nanometres (nm) or in the case of electrical capacitance, 100 nanofarads (nF) |
n |
1000−3 |
10−9 This list compares various sizes of positive numbers, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the so called short scale which is used in English speaking countries, as well as a name in the long scale which is used in a series of countries that do not have English as their national |
0.000000001 |
Billionth |
Milliardth |
1960 |
| pico Derived from the Italian piccolo, meaning small, this was one of the original 12 prefixes defined in 1960 when the International System of Units was established |
p |
1000−4 |
10−12 This list compares various sizes of positive numbers, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the so called short scale which is used in English speaking countries, as well as a name in the long scale which is used in a series of countries that do not have English as their national |
0.000000000001 |
Trillionth |
Billionth |
1960 |
| femto Femto- is a prefix in the metric system denoting a factor of 10−15 or 0.000000000000001. Adopted by the 11th Conférence Générale des Poids et Mesures, it was added in 1964 to the SI. It is derived from the Danish word femten, meaning "fifteen" |
f |
1000−5 |
10−15 This list compares various sizes of positive numbers, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the so called short scale which is used in English speaking countries, as well as a name in the long scale which is used in a series of countries that do not have English as their national |
0.000000000000001 |
Quadrillionth |
Billiardth |
1964 |
| atto Atto- is a prefix in the metric system denoting a factor of 10−18 or 0.000000000000000001 |
a |
1000−6 |
10−18 This list compares various sizes of positive numbers, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the so called short scale which is used in English speaking countries, as well as a name in the long scale which is used in a series of countries that do not have English as their national |
0.000000000000000001 |
Quintillionth |
Trillionth |
1964 |
| zepto Zepto- is a prefix in the metric system denoting a factor of 10−21 or 0.000000000000000000001 |
z |
1000−7 |
10−21 This list compares various sizes of positive numbers, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the so called short scale which is used in English speaking countries, as well as a name in the long scale which is used in a series of countries that do not have English as their national |
0.000000000000000000001 |
Sextillionth |
Trilliardth |
1991 |
| yocto |
y |
1000−8 |
10−24 This list compares various sizes of positive numbers, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the so called short scale which is used in English speaking countries, as well as a name in the long scale which is used in a series of countries that do not have English as their national |
0.000000000000000000000001 |
Septillionth |
Quadrillionth |
1991 |
- The metric system was introduced in 1795 with six prefixes. The other dates relate to recognition by a resolution of the CGPM The General Conference on Weights and Measures is the English name of the Conférence générale des poids et mesures . It is one of the three organizations established to maintain the International System of Units (SI) under the terms of the Convention du Mètre (Metre Convention) of 1875. It meets in Sèvres (in the southwestern suburbs of Paris).
- The 1948 recognition of the micron A micrometre is one millionth of a metre, or equivalently one thousandth of a millimetre or one thousand nanometres. It can also be written in scientific notation as 1×10−6 m, meaning 1⁄1000000 m by the CGPM was abrogated in 1967.
|
Examples
- 5 cm = 5×10−2 m = 5×0.01m = 0.05m
- 3 MW = 3×106 W = 3×1000000W = 3000000W
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 equals 1000 metres, 1 kilogram equals 1000 grams, 1 kilowatt equals 1000 watts, 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, for which the SI base unit (which is the kilogram, not the gram) already contains a prefix. So milligram (mg) is used instead of microkilogram (µkg), for example.
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 (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)." [2] 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." [3]
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." However the use of prefixed forms of "°C" (such as "µ°C") has not been adopted in science and engineering; prefixed forms of the kelvin are usually used instead.
Exponentiation of symbols
When units occur in exponentiation, for example, in square and cubic forms, any size prefix is considered part of the unit, and thus included in the exponentiation.
Pronunciation
There are two accepted pronunciations for the prefix giga-: /ˈɡɪɡə/ and /ˈdʒɪɡə/. According to the American writer Kevin Self, in the 1920s a German committee member of the International Electrotechnical Commission 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). [4] [5]
When an SI 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, gigabyte is pronounced /ˈɡɪɡəbaɪt/, with stress on the first syllable. However, words in common use outside the scientific community may follow idiosyncratic stress rules. For example, kilometre is commonly pronounced /kɨˈlɒmɨtər/, with reduced vowels on both syllables of metre.
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