How Many? A Dictionary of Units of Measurement
© Russ Rowlett and the University of North Carolina at Chapel Hill

Table of Contents
About the Dictionary
Using the Dictionary

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 © 2001 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