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 discu