# Prefixes

A powerful feature of the metric system is its use of prefixes. The SI prefixes consist of a set of names and symbols that can be prepended to any SI unit’s name or symbol to modify its value. All SI prefixes have values that are multiples or submultiples of powers of 10. When prepended to a unit, the value of the unit is multiplied by the value of the prefix. For example the prefix “kilo”, symbol “k”, prepended to the unit “metre”, symbol “m”, gives a modified unit “kilometre”, symbol “km”, that has a value equal to 1000 metres.

With the exception of centi, deci, deca and hecto, each SI prefix has a value of 1000n, where n is a non-zero integer from -10 to 10. The SI prefixes allow SI units to address very small and very large scales without numbers becoming cumbersome. The scales addressable by the standard SI prefixes have a range of 60 orders of magnitude, or 1060.

##### SI prefixes
 SI prefix Symbol Value quetta Q 1030 100010 1 000 000 000 000 000 000 000 000 000 000 ronna R 1027 10009 1 000 000 000 000 000 000 000 000 000 yotta Y 1024 10008 1 000 000 000 000 000 000 000 000 zetta Z 1021 10007 1 000 000 000 000 000 000 000 exa E 1018 10006 1 000 000 000 000 000 000 peta P 1015 10005 1 000 000 000 000 000 tera T 1012 10004 1 000 000 000 000 giga G 109 10003 1 000 000 000 mega M 106 10002 1 000 000 kilo k 103 10001 1 000 hecto h 102 100 deca da 101 10 100 10000 1 deci d 10-1 0.1 centi c 10-2 0.01 milli m 10-3 1000−1 0.001 micro µ 10-6 1000−2 0.000 001 nano n 10-9 1000−3 0.000 000 001 pico p 10-12 1000−4 0.000 000 000 001 femto f 10-15 1000−5 0.000 000 000 000 001 atto a 10-18 1000−6 0.000 000 000 000 000 001 zepto z 10-21 1000−7 0.000 000 000 000 000 000 001 yocto y 10-24 1000−8 0.000 000 000 000 000 000 000 001 ronto r 10-27 1000−9 0.000 000 000 000 000 000 000 000 001 quecto q 10-30 1000−10 0.000 000 000 000 000 000 000 000 000 001

Prefix symbols are printed in roman (upright) type, as are unit symbols, regardless of the type used in the surrounding text, and are attached to unit symbols without a space between the prefix symbol and the unit symbol. With the exception of da (deca), h (hecto), and k (kilo), all multiple prefix symbols are capital (upper case) letters, and all submultiple prefix symbols are lower case letters. All prefix names are printed in lower case letters, except at the beginning of a sentence.

The grouping formed by a prefix symbol attached to a unit symbol constitutes a new inseparable unit symbol (forming a multiple or submultiple of the unit concerned) that can be raised to a positive or negative power and that can be combined with other unit symbols to form compound unit symbols.

Similarly, prefix names are also inseparable from the unit names to which they are attached. Thus, for example, millimetre, micropascal, and meganewton are single words.

When units include exponents, for example, in square and cubic forms, the prefix is included in the exponentiation. For example, 1 km2 means one square kilometre, or the area of a square 1000 m × 1000 m, i.e. (1000 m)2, and not 1000 (m)2.

##### Examples
 2.3 cm3 = 2.3 (cm)3 = 2.3 (10–2 m)3 = 2.3 × 10–6 m3 1 cm–1 = 1 (10–2 m)–1 = 102 m–1 = 100 m−1 1 V/cm = (1 V)/(10–2 m) = 102 V/m = 100 V/m 5000 μs−1 = 5000 (μs)−1 = 5000 (10−6 s)−1 = 5 × 109 s−1

Compound prefix symbols, that is, prefix symbols formed by the juxtaposition of two or more prefix symbols, are not permitted. This rule also applies to compound prefix names.

Prefix symbols can neither stand alone nor be attached to the number 1, the symbol for the unit one. Similarly, prefix names cannot be attached to the name of the unit one, that is, to the word “one”.

Prefix names and symbols are used with a number of non-SI units, but they are never used with the non-SI units of time: minute (min), hour (h), day (d). However astronomers use milliarcsecond, which they denote mas, and microarcsecond, μas, which they use as units for measuring very small angles.

### Information technology

Units used in the field of information technology are not included in the SI. These units include the bit, byte and pixel, and derived units such as bit per second, and byte per second. When SI prefixes are used with these units, they should be used only when referring strictly to multiples of powers of 10.

### Binary prefixes

In information technology, it is often convenient to handle quantities in multiples of powers of 2, such as 210, or 1024. To avoid the incorrect usage of SI prefixes for multiples of powers of 2, there is a set of binary-based multiple prefixes, approved by the International Electrotechnical Commission (IEC), which should be used. For example, one kibibit is equal to 1024 bits, whereas one kilobit should refer only to 1000 bits. The rules for the use of binary prefixes are similar to those of the SI prefixes.

Binary prefixes should not be used with SI units.

##### IEC binary prefixes
 IEC prefix Symbol Value quebi Qi 2100 102410 1 267 650 600 228 229 401 496 703 205 376 robi Ri 290 10249 1 237 940 039 285 380 274 899 124 224 yobi Yi 280 10248 1 208 925 819 614 629 174 706 176 zebi Zi 270 10247 1 180 591 620 717 411 303 424 exbi Ei 260 10246 1 152 921 504 606 846 976 pebi Pi 250 10245 1 125 899 906 842 624 tebi Ti 240 10244 1 099 511 627 776 gibi Gi 230 10243 1 073 741 824 mebi Mi 220 10242 1 048 576 kibi Ki 210 10241 1 024 Note: The symbol for kibi is Ki, not ki.

The value of each binary prefix is equal to 1024n, where n is a positive integer from 1 to 10. The name of the prefix is a portmanteau formed from the first two letters of the SI prefix whose value is equal to 1000n, and the first two letters of the word “binary”

Each binary prefix symbol is formed from the uppercase version of the first letter of the prefix name followed by the lower case letter “i”.

##### Examples
 12 kilobits per second = 12 kbit/s = 12 × 10001 bit/s = 12 000 bits per second 12 kibibits per second = 12 Kibit/s = 12 × 10241 bit/s = 12 288 bits per second 8 megabytes per second = 8 MB/s = 8 × 10002 B/s = 8 000 000 bytes per second 8 mebibytes per second = 8 MiB/s = 8 × 10242 B/s = 8 388 608 bytes per second 4.5 gigabytes = 4.5 GB = 4.5 × 10003 B = 4 500 000 000 bytes 4.5 gibibytes = 4.5 GiB = 4.5 × 10243 B = 4 831 838 208 bytes

Although binary prefixes are not part of the SI, they are described here to avoid the incorrect usage of SI prefixes in the field of information technology.