SI prefixes are the unit prefixes which precede a basic unit of measure to indicate a decadic multiple or fraction of the unit. 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 dating back to the system's introduction in the 1790s. Today the prefixes are standardized for use in SI by BIPM in resolutions dating from 1960 to 1991. Since 2009, they have formed part of the International System of Quantities.
By now the BIPM specifies twenty prefixes for SI.
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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 arithmetic of measurements having prefixed units, the prefixes must be expanded to their numeric multiplier, except when adding or subtracting values with identical units. Hence, 5 mV × 5 mA =5E-3 V × 5E-3 A = 25E-6 W = 25 µW.
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 were commonly used for everyday purposes; especially the centimeter (cm) is common.
However, some modern building codes require that the millimetre be used in preference to the centimetre, because "use of centimeters leads to extensive usage of decimal points and confusion".
When units occur in exponentiation, for example, in square and cubic forms, the multiplication prefix must be considered part of the unit, and thus included in the exponentiation.
- 1 km² means one square kilometre, or the area of a square of 1000 m by 1000 m and not 1000 square metres.
- 2 Mm³ means two cubic megametres, or the volume of two cubes of 1000000 m by 1000000 m by 1000000 m or 2E+18 m³, and not 2000000 cubic metres (2E+6 m³).
Examples:
- 5 cm = 5×10−2 m = 5E-2 m = 0.05 m
- 9 km² = 9 × (km)² = 9 × (10³ m)² = 9 × (10³)² × m² = 9E+6 m² = 9 × 1000000 m² = 9000000 m²
- 3 MW = 3E+6 W = 3 × 1000000 W = 3000000 W
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).
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, though they remain valid combinations. In most contexts only a few most common combinations are established as standard.
Here are some special situations when using SI prefixes.
Mass:
The kilogram, gram, milligram, microgram, and smaller are common. However, megagram (and gigagram, teragram, etc.) are rarely used; tonnes (and kilotonnes, megatonnes, etc.) or scientific notation are used instead. Megagram is occasionally used to disambiguate the metric tonne from the various non-metric tons. An exception is pollution 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:
The litre, millilitre (equal to a cubic centimetre), microlitre, and smaller are common. In Europe, the centilitre is often used for packaged products but the use of the decilitre is rare everywhere. (The latter two items include prefixes corresponding to an exponent that is not divisible by three.)
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).
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 angstrom (equal to 0.1 nm) historically competed with the nanometre. The femtometre, used mainly in particle physics, is usually called a fermi. For large scales, megametre, gigametre, and larger are rarely used. Often used are astronomical units, light years, and parsecs; the astronomical unit is mentioned in the SI standards as an accepted non-SI unit.
Time and angles:
The 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.
Official policies about the use of these prefixes vary slightly between BIPM and the 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."
Temperature:
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." 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).
In this post we talked about the SI prefixes and its usage. Now we can describe the numbers with just a prefix in a unit. But sometimes it is still inconvenient with only these SI units. In the next post we will introduce some non-SI units accepted by SI.
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