Metric prefixes

Explanation of prefixes

A metric prefix is a convenient way of expressing mulitiples and subdivisions (larger and smaller) of any defined unit. In metric that means multiplying or dividing by 10, 100, 1000, etc. It consists of a partial word like “kilo” or “milli”.

For example, the prefix “kilo” means “times a thousand” or “one thousand of” the units in question. So “kilometre” means one thousand metres, and “kilogram” means one thousand grams.

Likewise, they can mean a fraction of a unit rather than a multiple. For example, the prefix “milli” means “one thousandth of”. So a millimetre is one thousandth of a metre. Put another way, there are one thousand millimetres in a metre.

These prefixes can be applied to any fundamental metric unit like the metre for distance, the gram for mass or weight, the watt for power, and so on.

Why use prefixes instead of distinct names?

Traditional measurement units that were used before the metric system had their own distinct names like stone, pound and ounce for weight or yard, foot and inch for distance. Some people criticise the metric system because of the long multisyllable names it gives rise to as a result of the prefixes. They do not exactly “trip off the tongue” or lend themselves to poetry.

This minor inconvenience has to be weighed against the more important advantages which are:

  1. The names are self explanatory. The two part name construction exposes the fundamental unit to which the named unit is referenced and by a factor which is encoded by the name itself.
  2. The names are easier to learn and remember. Only the set of prefixes need to be learned which can then be applied to any type of measurement. If distinct names were used there would be a plethora of names to learn for each type of measurement.
  3. The prefixes have a structure. The multiples and subdivisions are related by a consistent structure that is easy to understand. Most of the prefixes are related by multiples of 1000. A few which are seldom used nowadays are related by the compatible numbers 10 and 100.
  4. Prefixes are understood internationally. A standard set of symbols correspond to the metric prefixes (e.g. k- for kilo- and m- for milli-). They are recognised internationally and are independent of language.

SI Prefixes

Common prefixes

The table below includes the most commonly encountered prefixes based on multiples or subdivisions of 1000.

Prefix Symbol Multiple Examples
kilo k 1000 kilometre (km),
kilogram (kg),
kilowatt (kW)
mega M 1 000 000
(1 million)		 megawatt (MW) radio transmitter output,
megahertz (MHz) FM radio frequencies
giga G 1 000 000 000
(1 billion)		 gigawatt (GW) power station output,
gigahertz (GHz) computer processor speed
Prefix Symbol Fraction Examples
milli m 1/1000 millimetre (mm),
millilitre (ml or mL),
milligram (mg) drug doses
micro μ 1/1 000 000
(0.000 001)		 micrometre (µm)
precision engineeering,
microgram (µg) drug doses
nano n 1/1 000 000 000
(0.000 000 001)		 nanometre (nm)

Note that the examples merely illustrate typical usage and are not exhaustive.

The less commonly used prefixes with multiples and subdivisions between 1/1000 and 1000.

Prefix Symbol Multiple Examples
deca da 10 Rarely used
hecto h 100 hectolitre (hl or hL) – used to measure wine production

‘hectare’ (ha) is in fact a contraction of ‘hecto are’ where the ‘are’ is an old unit of area equal to 100 square metres (10 m × 10 m).

Hence 1 ha = 100 m × 100 m, which is 10 000 m2
Prefix Symbol Fraction Examples
deci d 1/10
(0.1)		 decilitre (dl or dL) sometimes used for blood sugar levels (mg/dL)
centi c 1/100
(0.01)		 centimetre (cm),
centilitre (cl or cL) wine bottles

Complete list

The table below is the complete list of all SI prefixes and their factors using exponential (scientific) notation.

Prefix Symbol Value Value name
quetta Q 1030 nonillion
ronna R 1027 octillion
yotta Y 1024 septillion
zetta Z 1021 sextillion
exa E 1018 quintillion
peta P 1015 quadrillion
tera T 1012 trillion
giga G 109 billion
mega M 106 million
kilo k 103 thousand
hecto h 102 hundred
deca da 101 ten
100 one
deci d 10-1 tenth
centi c 10-2 hundredth
milli m 10-3 thousandth
micro μ 10-6 millionth
nano n 10-9 billionth
pico p 10-12 trillionth
femto f 10-15 quadrillionth
atto a 10-18 quintillionth
zepto z 10-21 sextillionth
yocto y 10-24 septillionth
ronto r 10-27 octillionth
quecto q 10-30 nonillionth

Large numbers

The UK, in common with most other English-speaking countries, uses the short scale naming system for integer powers of ten. In the short scale system, one billion is equal to 1000 million, and one trillion is equal to 1000 billion, etc.

Before 1975, the long scale system was also in use, in which one billion was equal to 1 000 000 million, and one trillion was equal to 1 000 000 billion, etc. However, by the 1950s the short scale system was becoming increasingly prevalent, leading to confusion over how words like billion and trillion should be interpreted. This confusion effectively ended on 20 December 1974, when Prime Minister Harold Wilson stated that all UK Government statistics would henceforth use the short scale exclusively. In a written answer to the House of Commons, he explained,

“The word “billion” is now used internationally to mean 1000 million and it would be confusing if British Ministers were to use it in any other sense.”

The BBC and other media organisations were quick to follow the Prime Minister’s lead, and it soon became unnecessary to explain the intended meaning of words like billion and trillion.

Apart from being the de facto standard for English-speaking countries, the short scale naming system has the advantage of corresponding to metric prefixes better than the old long scale system.

Prefix Value Value name
quetta 1030 100010 nonillion
ronna 1027 10009 octillion
yotta 1024 10008 septillion
zetta 1021 10007 sextillion
exa 1018 10006 quintillion
peta 1015 10005 quadrillion
tera 1012 10004 trillion
giga 109 10003 billion
mega 106 10002 million
kilo 103 10001 thousand