Unit Prefixes - Maple Help

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 $\mathrm{\mu }$, 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 $\mathrm{\mu }$. 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 ${10}^{3}=1000$ is approximately equal to ${2}^{10}=1024$, 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.

 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 2^70 zebi Zi 1 zebibyte = ZiB = 1180591620717411303424 bytes 2^80 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.

Examples

 > $\mathrm{convert}\left(1,'\mathrm{units}','\mathrm{km}','\mathrm{cm}'\right)$
 ${100000}$ (1)
 > $\mathrm{convert}\left(1,'\mathrm{units}',\frac{'\mathrm{dm}'}{'\mathrm{ms}'},\frac{'\mathrm{Tm}'}{'h'}\right)$
 $\frac{{9}}{{25000000}}$ (2)
 > $\mathrm{convert}\left(1,'\mathrm{units}','\mathrm{bytes}','\mathrm{kibibyte}'\right)$
 $\frac{{1}}{{1024}}$ (3)
 > $\mathrm{Units}\left[\mathrm{AddUnit}\right]\left('\mathrm{byte}','\mathrm{symbol}'='B'\right)$
 > $\mathrm{convert}\left(1,'\mathrm{units}','\mathrm{MiB}','B'\right)$
 ${1048576}$ (4)
 > $\mathrm{select}\left(x↦\mathrm{type}\left(x,\mathrm{identical}\left(\mathrm{prefix}\right)=\mathrm{anything}\right),\left[\mathrm{Units}:-\mathrm{GetUnit}\left('\mathrm{second}'\right)\right]\right)$
 $\left[{\mathrm{prefix}}{=}{\mathrm{SI}}\right]$ (5)
 > $\mathrm{select}\left(x↦\mathrm{type}\left(x,\mathrm{identical}\left(\mathrm{prefix}\right)=\mathrm{anything}\right),\left[\mathrm{Units}:-\mathrm{GetUnit}\left('\mathrm{hour}'\right)\right]\right)$
 $\left[{\mathrm{prefix}}{=}{\mathrm{false}}\right]$ (6)
 > $\mathrm{select}\left(x↦\mathrm{type}\left(x,\mathrm{identical}\left(\mathrm{prefix}\right)=\mathrm{anything}\right),\left[\mathrm{Units}:-\mathrm{GetUnit}\left('\mathrm{byte}'\right)\right]\right)$
 $\left[{\mathrm{prefix}}{=}{\mathrm{IEC}}\right]$ (7)