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.)

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.