Metric and SI Unit Prefixes

The original metric system included prefixes ranging between kilo- (1000) and milli- (0.001). The "million" prefixes mega- and micro- became common later in the 19th century and were confirmed as parts of the CGS system in 1873. Since the establishment of the International System of Units in 1960 there have been four extensions of the lsit of prefixes, the most recent being in 1991.

Here are the metric prefixes, with their numerical equivalents stated in the American system for naming large numbers and the dates of their approval.

yotta- (Y-) 1024 1 septillion 19th General Conference, 1991
zetta- (Z-) 1021 1 sextillion 19th General Conference, 1991
exa- (E-) 1018 1 quintillion 15th General Conference, 1975
peta- (P-) 1015 1 quadrillion 15th General Conference, 1975
tera- (T-) 1012 1 trillion 11th General Conference, 1960
giga- (G-) 109 1 billion 11th General Conference, 1960
mega- (M-) 106 1 million CGS System, 1873
kilo- (k-) 103 1 thousand Original metric system, 1795
hecto- (h-) 102 1 hundred Original metric system, 1795
deka- (da-)** 10 1 ten Original metric system, 1795
deci- (d-) 10-1 1 tenth Original metric system, 1795
centi- (c-) 10-2 1 hundredth Original metric system, 1795
milli- (m-) 10-3 1 thousandth Original metric system, 1795
micro- (µ-) 10-6 1 millionth CGS System, 1873
nano- (n-) 10-9 1 billionth 11th General Conference, 1960
pico- (p-) 10-12 1 trillionth 11th General Conference, 1960
femto- (f-) 10-15 1 quadrillionth 12th General Conference, 1964
atto- (a-) 10-18 1 quintillionth 12th General Conference, 1964
zepto- (z-) 10-21 1 sextillionth 19th General Conference, 1991
yocto- (y-) 10-24 1 septillionth 19th General Conference, 1991

 

Notes:

Before the expansion of the prefix list in 1960 there was a proliferation of double prefixes such as micromicro- for 10-12 and kilomega- for 109. The introduction of new prefixes made these constructions unnecessary, and the International System now prohibits them.

I am often asked about prefixes for other multiples, such as 104, 105, 10-4, and 10-5. The prefix myria- (my-) for 104 was included in the original metric system and dimi- (dm-), a contraction of decimilli-, was sometimes used for 10-4, but these prefixes are now obsolete and are not accepted in the SI. To the best of my knowledge, no prefixes were ever accepted generally for 105, or 10-5.

There is a widespread misconception that prefixes for positive powers of ten are all capitalized, leading to the use of K- for kilo- and D- for deca-. Although this does seem like a useful idea, it is not correct.

**The SI Brochure spelling of this prefix is deca-, but the U.S. National Institute of Standards and Technology (NIST) recommends deka-. National variations in spelling of the prefixes are allowed by the SI. In Italian, for example, hecto- is spelled etto- and kilo- is spelled chilo-. The symbols, however, are the same in all languages, so dam (not dkm) is the symbol for the dekameter and km is the symbol for the Italian chilometro.

The prefixes hecto-, deka-, deci-, and centi- are widely used in everyday life but are generally avoided in scientific work. Contrary to the belief of some scientists, however, the SI does allow use of these prefixes.

The last letter of a prefix is often omitted if the first letter of the unit name is a vowel, causing the combination to be hard to pronounce otherwise. Thus 100 ares is a hectare and 1 million ohms is a megohm. However, the last letter of the prefix is not omitted if pronunciation is not a problem, as in the case of the milliampere. The letter "l" is sometimes added to prefixes before the erg, so 1 million ergs is a megalerg (sounds odd, but better than "megerg").

Binary prefixes

In computing, a custom arose of using the metric prefixes to specify powers of 2. For example, a kilobit was sometimes 210 = 1024 bits instead of 1000 bits. This practice led, and still leads, to considerable confusion. In an effort to eliminate this confusion, in 1998 the International Electrotechnical Commission approved new prefixes for the powers of 2. These prefixes are as follows:

kibi- Ki- 210 = 1 024
mebi- Mi- 220 = 1 048 576
gibi- Gi- 230 = 1 073 741 824
tebi- Ti- 240 = 1 099 511 627 776
pebi- Pi- 250 = 1 125 899 906 842 624
exbi- Ei- 260 = 1 152 921 504 606 846 976

The Commission's ruling is that the standard metric prefixes should be used in computing just as they are used in other fields. Thus, 32 gigabytes (GB) means exactly 32 000 000 000 bytes, and 32 gibibytes (GiB) means exactly 34 359 738 368 bytes.

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Revised April 26, 2018