Names for Large Numbers

The English names for large numbers are coined from the Latin names for small numbers n by adding the ending -illion suggested by the name "million." Thus billion and trillion are coined from the Latin prefixes bi- (n = 2) and tri- (n = 3), respectively. In the American system for naming large numbers, the name coined from the Latin number n applies to the number 103n+3. In a system traditional in many European countries, the same name applies to the number 106n.

In particular, a billion is 109 = 1 000 000 000 in the American system and 1012 = 1 000 000 000 000 in the European system. For 109, Europeans say "thousand million" or "milliard."

Although we describe the two systems today as American or European, both systems are actually of French origin. The French physician and mathematician Nicolas Chuquet (1445-1488) apparently coined the words byllion and tryllion and used them to represent 1012 and 1018, respectively, thus establishing what we now think of as the "European" system. However, it was also French mathematicians of the 1600's who used billion and trillion for 109 and 1012, respectively. This usage became common in France and in America, while the original Chuquet nomenclature remained in use in Britain and Germany. The French decided in 1948 to revert to the Chuquet ("European") system, leaving the U.S. as the chief standard bearer for what then became clearly an American system.

In recent years, American usage has eroded the European system, particularly in Britain and to a lesser extent in other countries. This is primarily due to American finance, because Americans insist that $1 000 000 000 be called a billion dollars. In 1974, the government of Prime Minister Harold Wilson announced that henceforth "billion" would mean 109 and not 1012 in official British reports and statistics. The Times of London style guide now defines "billion" as "one thousand million, not a million million."

The result of all this is widespread confusion. Anyone who uses the words "billion" and "trillion" internationally should make clear which meaning of those words is intended. On the Internet, some sites outside the U.S. use the compound designation "milliard/billion" to designate the number 1 000 000 000. In science, the names of large numbers are usually avoided completely by using the appropriate SI prefixes. Thus 109 watts is a gigawatt and 1012 joules is a terajoule. Such terms cannot be mistaken.

There is no real hope of resolving the controversy in favor of either system. Americans are not likely to adopt the European nomenclature, and Europeans will always regard the American system as an imposition. However, it is possible to imagine a solution: junk both Latin-based systems and move to a Greek-based system in which, for n > 3, the Greek number n is used to generate a name for 103n. (The traditional names thousand and million are retained for n = 1 and 2 and the special name gillion, suggested by the SI prefix giga-, is proposed for n = 3.)

n =
103n =
American
name
European
name
SI prefix
Greek-based
name
(proposed)
3
109
billion
milliard
giga-
gillion
4
1012
trillion
billion
tera-
tetrillion
5
1015
quadrillion
billiard
peta-
pentillion
6
1018
quintillion
trillion
exa-
hexillion
7
1021
sextillion
trilliard
zetta-
heptillion
8
1024
septillion
quadrillion
yotta-
oktillion
9
1027
octillion
quadrilliard
ennillion
10
1030
nonillion
quintillion
dekillion
11
1033
decillion
quintilliard
hendekillion
12
1036
undecillion
sextillion
dodekillion
13
1039
duodecillion
sextilliard
]
trisdekillion
14
1042
tredecillion
septillion
tetradekillion
15
1045
quattuordecillion
septilliard
pentadekillion
16
1048
quindecillion
octillion
hexadekillion
17
1051
sexdecillion
octilliard
heptadekillion
18
1054
septendecillion
nonillion
oktadekillion
19
1057
octodecillion
nonilliard
enneadekillion
20
1060
novemdecillion
decillion
icosillion
21
1063
vigintillion
decilliard
icosihenillion
22
1066
unvigintillion
undecillion
icosidillion
23
1069
duovigintillion
undecilliard
icositrillion
24
1072
trevigintillion
duodecillion
icositetrillion
25
1075
quattuorvigintillion
duodecilliard
icosipentillion
26
1078
quinvigintillion
tredecillion
icosihexillion
27
1081
sexvigintillion
tredecilliard
icosiheptillion
28
1084
septenvigintillion
quattuordecillion
icosioktillion
29
1087
octovigintillion
quattuordecilliard
icosiennillion
30
1090
novemvigintillion
quindecillion
triacontillion
31
1093
trigintillion
quindecilliard
triacontahenillion
32
1096
untrigintillion
sexdecillion
triacontadillion
33
1099
duotrigintillion
sexdecilliard
triacontatrillion

This process can be continued indefinitely, but one has to stop somewhere. The name centillion (n = 100) has appeared in many dictionaries. A centillion is 10303 (1 followed by 303 zeroes) in the American system and a whopping 10600 (1 followed by 600 zeroes) in the European system.

Finally, there is the googol, the number 10100 (1 followed by 100 zeroes). Invented more for fun than for use, the googol lies outside the regular naming systems. The googol equals 10 duotrigintillion in the American system, 10 sexdecilliard in the European system, and 10 triacontatrillion in the proposed Greek-based system.

The googolplex (1 followed by a googol of zeroes) is far larger than any of the numbers discussed here.

 

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All material in this folder is copyright 2018 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time.

November 1, 2001. Revised April 28, 2018.