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Unit Prefixes

Description

• 

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.

International System of Units (SI)

Factor

Prefix

Symbol

Adopted

Etymology

 

 

 

 

 

10^24

yotta

Y

1991

otto, eight in Italian

10^21

zetta

Z

1991

sette, seven in Italian

10^18

exa

E

1975

hex, six in Greek

10^15

peta

P

1975

pente, five in Greek

10^12

tera

T

1960

teras, monster in Greek

10^9

giga

G

1960

gigas, giant in Greek

10^6

mega

M

1960

megas, huge in Greek

1000

kilo

k

1795

khilioi, thousand in Greek

100

hecto

h

1795

hekaton, hundred in Greek

10

deka

da, dk

1795

deka, ten in Greek

 

 

 

 

 

1/10

deci

d

1795

decimus, tenth in Latin

1/100

centi

c

1795

centum, hundred in Latin

1/1000

milli

m

1795

mille, thousand in Latin

10^(-6)

micro

mu, u, mc

1960

mikros, small in Greek

10^(-9)

nano

n

1960

nanos, dwarf in Greek

10^(-12)

pico

p

1960

piccolo, little bit in Spanish

10^(-15)

femto

f

1964

femten, 15 in Norwegian/Danish

10^(-18)

atto

a

1964

atten, 18 in Norwegian/Danish

10^(-21)

zepto

z

1991

sept, seven in Greek

10^(-24)

yocto

y

1991

okto, eight in Greek

 

 

 

 

 

• 

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 m. 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.

International Electrotechnical Commission (IEC)

• 

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 the following list of binary powers:

Factor

Prefix

Symbol

Example

 

 

 

 

2^10

kibi

Ki

1 kibibyte = KiB = 1024 bytes

2^20

mebi

Mi

1 mebibyte = MiB = 1048576 bytes

2^30

gibi

Gi

1 gibibyte = GiB = 1073741824 bytes

2^40

tebi

Ti

1 tebibyte = TiB = 1099511627776 bytes

2^50

pebi

Pi

1 pebibyte = PiB = 1125899906842624 bytes

2^60

exbi

Ei

1 exbibyte = EiB = 1152921504606846976 bytes

 

 

 

 

• 

The progression of Ki, Mi, Gi, Ti, Pi, and Ei is similar to that of the SI prefixes, k, M, G, T, P, and E, 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.

Examples

convert1,'units','km','cm'

100000

(1)

convert1,'units','dm''ms','Tm''h'

925000000

(2)

convert1,'units','bytes','kibibyte'

11024

(3)

Units[AddUnit]'byte','symbol'='B'

convert1,'units','MiB','B'

1048576

(4)

selectx→typex,identicalprefix=anything,Units:-GetUnit'second'

prefix=SI

(5)

selectx→typex,identicalprefix=anything,Units:-GetUnit'hour'

prefix=false

(6)

selectx→typex,identicalprefix=anything,Units:-GetUnit'byte'

prefix=IEC

(7)

See Also

convert/units, Units, Units/AddUnit, Units/Index


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