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NAME
units - decimal and binary prefixes
DESCRIPTION
Decimal prefixes
The SI system of units uses prefixes that indicate powers of ten. A kilometer is 1000
meter, and a megawatt is 1000000 watt. Below the standard prefixes.
Prefix Name Value
q quecto 10^-30 = 0.000000000000000000000000000001
r ronto 10^-27 = 0.000000000000000000000000001
y yocto 10^-24 = 0.000000000000000000000001
z zepto 10^-21 = 0.000000000000000000001
a atto 10^-18 = 0.000000000000000001
f femto 10^-15 = 0.000000000000001
p pico 10^-12 = 0.000000000001
n nano 10^-9 = 0.000000001
µ micro 10^-6 = 0.000001
m milli 10^-3 = 0.001
c centi 10^-2 = 0.01
d deci 10^-1 = 0.1
da deka 10^ 1 = 10
h hecto 10^ 2 = 100
k kilo 10^ 3 = 1000
M mega 10^ 6 = 1000000
G giga 10^ 9 = 1000000000
T tera 10^12 = 1000000000000
P peta 10^15 = 1000000000000000
E exa 10^18 = 1000000000000000000
Z zetta 10^21 = 1000000000000000000000
Y yotta 10^24 = 1000000000000000000000000
R ronna 10^27 = 1000000000000000000000000000
Q quetta 10^30 = 1000000000000000000000000000000
The symbol for micro is the Greek letter mu, often written u in an ASCII context where
this Greek letter is not available.
Binary prefixes
The binary prefixes resemble the decimal ones, but have an additional 'i' (and "Ki" starts
with a capital 'K'). The names are formed by taking the first syllable of the names of
the decimal prefix with roughly the same size, followed by "bi" for "binary".
Prefix Name Value
Ki kibi 2^10 = 1024
Mi mebi 2^20 = 1048576
Gi gibi 2^30 = 1073741824
Ti tebi 2^40 = 1099511627776
Pi pebi 2^50 = 1125899906842624
Ei exbi 2^60 = 1152921504606846976
Zi zebi 2^70 = 1180591620717411303424
Yi yobi 2^80 = 1208925819614629174706176
Discussion
Before these binary prefixes were introduced, it was fairly common to use k=1000 and
K=1024, just like b=bit, B=byte. Unfortunately, the M is capital already, and cannot be
capitalized to indicate binary-ness.
At first that didn't matter too much, since memory modules and disks came in sizes that
were powers of two, so everyone knew that in such contexts "kilobyte" and "megabyte" meant
1024 and 1048576 bytes, respectively. What originally was a sloppy use of the prefixes
"kilo" and "mega" started to become regarded as the "real true meaning" when computers
were involved. But then disk technology changed, and disk sizes became arbitrary numbers.
After a period of uncertainty all disk manufacturers settled on the standard, namely
k=1000, M=1000 k, G=1000 M.
The situation was messy: in the 14k4 modems, k=1000; in the 1.44 MB diskettes, M=1024000;
and so on. In 1998 the IEC approved the standard that defines the binary prefixes given
above, enabling people to be precise and unambiguous.
Thus, today, MB = 1000000 B and MiB = 1048576 B.
In the free software world programs are slowly being changed to conform. When the Linux
kernel boots and says
hda: 120064896 sectors (61473 MB) w/2048KiB Cache
the MB are megabytes and the KiB are kibibytes.
SEE ALSO
The International System of Units ⟨https://www.bipm.org/documents/20126/41483022/
SI-Brochure-9.pdf⟩.