## 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.

You are welcome to email the author (rowlett@email.unc.edu) with comments and suggestions.

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