# Number words and prefixes

## Words for large numbers

By a curious historical confusion, two different systems for naming large numbers exist, one in the US and the other in Britain and other parts of the English-speaking world. This could be troublesome, but these days such large numbers are much more often given in unambiguous scientific notation, and the US usage is in any case coming to dominate, as it has almost completely with billion.

The original scheme, invented in France in the sixteenth century, started with million and multiplied 1 by that number the required number of times. The name of the unit was then based on the number of multiplications, using Latin numerals. So a sextillion was 1 multiplied by a million six times, making a number expressed by 1 followed by 36 zeroes (1036 in scientific notation).

In the eighteenth century French mathematicians changed to multiples of a thousand instead, but took over the existing number names; the Latin numbers then marked one less than the number of multiplications, so that trillion was 1 multiplied by a thousand four times. The US system was based on the thousands scheme, but the British stayed with the older millions one.

The following table gives some names and values in the two systems:

Number
word

Millions
scheme

Thousands
scheme

million

106

106

billion (Latin bi-, twice)

1012

109

trillion (Latin tres, three)

1018

1012

1024

1015

quintillion (Latin quinque, five)

1030

1018

sextillion (Latin sex, six)

1036

1021

septillion (Latin septem, seven)

1042

1024

octillion (Latin octo, eight)

1048

1027

nonillion (Latin nonus, ninth)

1054

1030

decillion (Latin decem, ten)

1060

1033

Two parallel sets of prefixes for number multiples exist, one derived from Latin, the other from Greek. These appear widely in compounds but are no longer much used to create new words, the job having been largely passed to the SI method described below, especially in scientific usage.

## International system of number prefixes

The standard system of prefixes for multiples these days is that laid down in SI units (Système International D’Unités), an international agreement dating from 1960, which defines standard units for quantities and the names for the decimal prefixes to use with them. These are widely used.

The standard SI prefixes for multiples are:

deca-

10

Greek deka, ten

hecto-

100

Greek hekaton, hundred

kilo-

103

Greek khilioi, thousand

mega-

106

Greek megas, great

giga-

109

Greek gigas, giant

tera-

1012

Greek teras, monster

peta-

1015

Greek penta-, five

exa-

1018

Based on Greek hexa-, six

zetta-

1021

Based on Latin septi‑, seven

yotta-

1024

Based on Latin octo‑, eight

ronna-

1027

Loosely based on Greek ennéa, nine

quetta-

1030

Loosely based on Latin decem, ten

The standard SI prefixes for fractional quantities are:

deci-

10-1

Latin decimus, a tenth

centi-

10-2

Latin centum, a hundred

milli-

10-3

Latin mille, thousand

micro-

10-6

Greek mikros, small

nano-

10-9

Greek nanos, dwarf

pico-

10-12

Spanish pico, literally a little bit

femto-

10-15

Danish or Norwegian femten, fifteen

atto-

10-18

Danish or Norwegian atten, eighteen

zepto-

10-21

Adapted from septi-, seven, on the pattern of other multiples

yocto-

10-24

ronto-

10-27

Loosely based on Greek ennéa, nine

quecto-

10-30

Loosely based on Latin decem, ten

The prefixes hecto-, deca-, deci-, and centi- are generally avoided in scientific work.

## Binary multiples for computer purposes

The use of decimal prefixes to describe the similar — but not identical — binary multiples used in computing (such as megabyte or terabit) has caused confusion — as a result of various conventions, a megabyte can be 1,048,576 or 1,024,000 or 1,000,000.

In 1998 the International Electrotechnical Commission (IEC) agreed an international standard for a new group of prefixes that removes the ambiguity; names use the first two letters of the SI decimal prefix, followed by the letters bi, for binary. These are only slowly coming into use.

kibi-

210

mebi-

220

gibi-

230

tebi-

240

pebi-

250

exbi-

260

zebi-

270

yobi-

280