A wide variety of large numbers crop up in mathematics. Some are contrived, but some actually arise in proofs. Often, it is possible to prove existence theorems by deriving some potentially huge upper limit which is frequently greatly reduced in subsequent versions (e.g., Graham's number, Kolmogorov-Arnold-Moser theorem, Mertens conjecture, Skewes number, Wang's conjecture).
Large decimal numbers beginning with 
are named according to two mutually conflicting nomenclatures:
the American system (in which the prefix stands for 
in 
)
and the British system (in which the prefix stands for 
in 
).
The British names for billion, trillion,
etc. originate from the late 15th century when the French physician and mathematician
Nicolas Chuquet (1445-1488) used the Latin prefixes to denote successive powers of
one million (
) and the suffix "-llion" to refer one million
(Rowlett). In more recent years, the "American" system has become widely
used in England as well as in the United States (The Chicago Manual of Style
2003). This constitutes a fortunate development for standardization of terminology,
albeit a somewhat regrettable development from the point of view that the British
convention for representing large numbers is simpler and more logical than the American
one.
The following table gives the names assigned to various powers of 10 (Woolf 1980).
| American | British | power of 10 |
| million | million |  |
| billion | milliard |  |
| trillion | billion |  |
| quadrillion |  | |
| quintillion | trillion |  |
| sextillion |  | |
| septillion | quadrillion |  |
| octillion |  | |
| nonillion | quintillion |  |
| decillion |  | |
| undecillion | sexillion |  |
| duodecillion |  | |
| tredecillion | septillion |  |
| quattuordecillion |  | |
| quindecillion | octillion |  |
| sexdecillion |  | |
| septendecillion | nonillion |  |
| octodecillion |  | |
| novemdecillion | decillion |  |
| vigintillion |  | |
| undecillion |  | |
| duodecillion |  | |
| tredecillion |  | |
| quattuordecillion |  | |
| quindecillion |  | |
| sexdecillion |  | |
| septendecillion |  | |
| octodecillion |  | |
| novemdecillion |  | |
| vigintillion |  | |
| centillion |  | |
| centillion |  |
