Unit Prefixes
Description
International System of Units (SI)
International Electrotechnical Commission (IEC)
Examples
References
To write multiples of units in an abbreviated form and avoid unnecessarily large or small powers, both the International System of Units (SI) and the International Electrotechnical Commission (IEC) have approved lists of prefixes that can be used in conjunction with certain units.
For each multiple, the prefix can be attached to the unit name and the prefix symbol can be attached to the unit symbol. For example, centimeter and cm. The prefix cannot be attached to the symbol and the prefix symbol cannot be attached to the unit name. For example, cmeter and centim are not accepted as units.
A prefix must be used in conjunction with a unit. It cannot be used to represent numerical values. For example, k does not represent 1000.
Prefixes cannot be combined into compound prefixes. For example, use nanometer, not millimicrometer.
The column titled Prefixes in the table describing the units of a given dimension, eg. length, shows whether a unit may be prefixed, and according to which of the conventions listed below. The ability to prefix a unit, and by which convention, can be determined programmatically using the GetUnit command.
Factor
Prefix
Symbol
Adopted
Etymology
1030
quetta
Q
2022
decem [1], ten in Latin
1027
ronna
R
ennea / novem [1], nine in Greek and Latin, resp.
1024
yotta
Y
1991
otto, eight in Italian
1021
zetta
Z
sette, seven in Italian
1018
exa
E
1975
hex, six in Greek
1015
peta
P
pente, five in Greek
1012
tera
T
1960
teras, monster in Greek
109
giga
G
gigas, giant in Greek
106
mega
M
megas, huge in Greek
1000
kilo
k
1795
khilioi, thousand in Greek
100
hecto
h
hekaton, hundred in Greek
10
deka
da, dk
deka, ten in Greek
1/10
deci
d
decimus, tenth in Latin
1/100
centi
c
centum, hundred in Latin
1/1000
milli
m
mille, thousand in Latin
10−6
micro
μ, u, mc
mikros, small in Greek
10−9
nano
n
nanos, dwarf in Greek
10−12
pico
p
piccolo, little bit in Spanish
10−15
femto
f
1964
femten, 15 in Norwegian/Danish
10−18
atto
a
atten, 18 in Norwegian/Danish
10−21
zepto
z
sept, seven in Greek
10−24
yocto
y
okto, eight in Greek
10−27
ronto
r
10−30
quecto
q
The correct symbol for the prefix deka is da, but dk is common in the United States. The correct symbol for the prefix micro is the greek letter μ. Because the SI does not give an acceptable alternative in an ASCII environment, three prefix symbols have gained acceptance in various fields: u, mu, and mc. Any of these prefix symbols is valid in the Units package.
In 1960, at the 10th CGPM, the prefix myria for 10000 was removed from the list of accepted prefixes.
The natural base for computers is 2. Since 103⁢=⁢1000 is approximately equal to 210⁢=⁢1024, the term kilobytes, referring to 1024 bytes, was accepted.
In 1998, to remove any possible confusion as to whether kilo refers to a multiplier of 1000 or 1024, the IEC approved a list of names and symbols for binary powers. This list was extended in 2005.
Example
210
kibi
Ki
1 kibibyte = KiB = 1024 bytes
220
mebi
Mi
1 mebibyte = MiB = 1048576 bytes
230
gibi
Gi
1 gibibyte = GiB = 1073741824 bytes
240
tebi
Ti
1 tebibyte = TiB = 1099511627776 bytes
250
pebi
Pi
1 pebibyte = PiB = 1125899906842624 bytes
260
exbi
Ei
1 exbibyte = EiB = 1152921504606846976 bytes
270
zebi
Zi
1 zebibyte = ZiB = 1180591620717411303424 bytes
280
yobi
Yi
1 yobibyte = YiB = 1208925819614629174706176 bytes
The progression of Ki, Mi, Gi, Ti, Pi, Ei, Zi, Yi is similar to that of the SI prefixes, k, M, G, T, P, E, Z, Y, though for consistency, Ki is capitalized.
Note that by default, the symbol B is reserved for unit bel. To change this, use the AddUnit routine.
convert⁡1,units,km,cm
100000
convert⁡1,units,dmms,Tmh
925000000
convert⁡1,units,bytes,kibibyte
11024
UnitsAddUnit⁡byte,symbol=B,default
convert⁡1,units,MiB,B
1048576
select⁡x↦type⁡x,identical⁡prefix=anything,Units:-GetUnit⁡second
prefix=SI
select⁡x↦type⁡x,identical⁡prefix=anything,Units:-GetUnit⁡hour
prefix=none
select⁡x↦type⁡x,identical⁡prefix=anything,Units:-GetUnit⁡byte
prefix=IEC
[1] R. Brown, Discussion on the possible extension of the available range of SI prefixes. BIPM CCU/2019-10_04.
See Also
convert/units
Units
Units/AddUnit
Units/Index
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