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# metric prefixes

## metric prefixes - definitions, values and symbols

The metric prefixes have entered many parts of our language and terminology, especially measurements and performance data of very big and very small things (gigabyte, microgram, nanosecond, etc). Knowing the actual values of the metric prefixes enables us to have a better understanding of the terms which use them, and the real size of things that are described by them.

In the metric prefixes table below, 'Factor' equates to the
ten-times factor; the positive ones represent the number of zeros after the
figure; the negatives show the number of decimal places after the decimal
point. E.g., kilogram = 10x10x10 = 10^{3} (10 to the power of three is
ten multiplied by itself three times = 1,000. A milligram is 1gm x
10^{-3} = one thousandth of a gram = 0.001gm).

The metric prefixes help us to appreciate measurements and sizes much more accurately: for example:

How heavy is a microgram? Could you feel a microgram in the palm of your hand?

I doubt it .... a microgram is actually just one-millionth of a gram.

How quick is a nanosecond? A blink of an eye?

A bit quicker..... about a billion passed while you are reading this sentence.

Here are some other common random words which include metric prefix words, which are interesting discussion points if you seek to explore numbers yourself, or especially if you are attempting to make the subject appealing and accessible to young people or trainees of others sorts.

- gigabytes, terabytes and petabytes in computing
- nanotechnology and nanobot
- micro-organisms, microwaves, micron, micrometer (although note that 'micro' also has the general meaning of small, from the Greek 'mikros')
- trillion (tn) as an increasingly used measure of monetary budget or debt or output of government and economy (fast-eclipsing the scale of billions and millions, which were once beyond imagination but are now are dwarfed by the extent of modern national and international finances)
- the words decimate and centurion from Roman times
- you and your students/trainees will no doubt think of plenty more examples..

Numbers and mathematics are fascinating and useful in work and life. We all need to understand numbers and maths to a level necessary for even the most basic tasks, such as balancing personal finances, completing expenses claims or tax returns, and assessing the best deals when we do our grocery shopping. To progress your career into management or other higher responsibility, or to start up and run your own business, a good understanding of mathematics is crucial - especially being capable with big numbers, and being sure where to put the decimal point in monetary calculations, where failing to do so can cause disastrous errors.

The metric prefixes offer a simple and quick way to introduce the main principles of decimals and big number calculations, as well as providing a meaningful reference by which to explore or teach most other aspects of mathematics.

See also the note below about short scale and long scale big number names. A billion does not mean the same number to everyone..

## the metric prefixes table

prefix |
symbol |
factors |
decimal number |
short scale*
(UK/US etc) |
long scale*
(Europe exc UK) |

deca |
da |
10^{1} |
10 | ten | ten |

hecto |
h |
10^{2} |
100 | hundred | hundred |

kilo |
k |
10^{3} |
1,000 | thousand | thousand |

mega |
M |
10^{6} |
1,000,000 | million | million |

giga |
G |
10^{9} |
1,000,000,000 | billion | milliard |

tera |
T |
10^{12} |
1,000,000,000,000 | trillion | billion |

peta |
P |
10^{15} |
1,000,000,000,000,000 | quadrillion | billiard |

exa |
E |
10^{18} |
1,000,000,000,000,000,000 | quintillion | trillion |

zetta |
Z |
10^{21} |
1,000,000,000,000,000,000,000 | sextillion | trilliard |

yotta |
Y |
10^{24} |
1,000,000,000,000,000,000,000,000 | septillion | quadrillion |

deci |
d |
10^{-1} |
0.1 | tenth | tenth |

centi |
c |
10^{-2} |
0.01 | hundredth | hundredth |

milli |
m |
10^{-3} |
0.001 | thousandth | thousandth |

micro |
µ |
10^{-6} |
0.000 001 | millionth | millionth |

nano |
n |
10^{-9} |
0.000 000 001 | billionth | milliardth |

pico |
p |
10^{-12} |
0.000 000 000 001 | trillionth | billionth |

femto |
f |
10^{-15} |
0.000 000 000 000 001 | quadrillionth | billiardth |

atto |
a |
10^{-18} |
0.000 000 000 000 000 001 | quintillionth | trillionth |

zepto |
z |
10^{-21} |
0.000 000 000 000 000 000 001 | sextillionth | trilliardth |

yocto |
y |
10^{-24} |
0.000 000 000 000 000 000 000 001 | septillionth | quadrillionth |

**Big number
names - short and long scale** - Generally 'long scale' names of numbers
are used in UK/US/Arabic-English-speaking nations. 'Short scale' number names
are used in mainland Europe and other non-English-speaking nations. Beyond a
million, short scale numbers are named in steps of 1,000-times the previous
number. For example, a billion is a thousand-millions. Long scale numbering
beyond a million use the short scale numbers in steps of 1,000,000-times the
previous number, so for example a billion is a million-millions. the
consequential intermediate steps in the long scale are named using 'ard' and
ardth' suffixes, so for example a thousand millions is called a milliard. If in
doubt it is important to clarify the local convention.

This metric prefixes page is one of the least amusing on this website, although it does provide a lot of interesting material for quizzes and trivia puzzles. If you're in the mood for something a little more light-hearted, then see: