Names of large numbers

The "standard dictionary numbers"

Throughout this article, exponential notation is used. 10⁶ could also be written as the number 1 followed by six 0's, 1 000 000; 10⁹ could be written as 1 000 000 000, and so on.

Names of numbers large than a quadrillion are almost never used, for reasons discussed further below. It is debatable which of them should be considered real working English vocabulary and which are merely trivia, curiosities, or coinages. The following table lists those names of numbers which are found in many English dictionaries and thus have a special claim to being "real words."

Name	American value	British value	Authorities
million	106	106	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993
milliard		109	√ AHD4, √ OED2
billion	109	1012	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993
trillion	1012	1018	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993
quadrillion	1015	1024	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993
quintillion	1018	1030	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993
sextillion	1021	1036	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993
septillion	1024	1042	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993
octillion	1027	1048	√ AHD4, √ OED2, √ OEDnew, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993
nonillion	1030	1054	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993
decillion	1033	1060	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993
undecillion	1036	1066	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993
duodecillion	1039	1072	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993
tredecillion	1042	1078	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993
quattuordecillion	1045	1084	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993
quindecillion	1048	1090	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993
sexdecillion	1051	1096	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993
septendecillion	1054	10102	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993
octodecillion	1057	10108	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993
novemdecillion	1060	10114	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993
vigintillion	1063	10120	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993
googol	10100	10100	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993
centillion	10303	10600	√ AHD4, √ OED2
googolplex	10googol	10googol	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993

Note the oddity that some dictionaries list "decillion" and "vigintillion," but not of the numbers in between (undecillion, duodecillion, etc.)

Vigintillion appears to be the highest name ending in -illion that is included in these dictionaries. Trigintillion, often cited as a word in discussions of names of large numbers, is not included in any of them; nor are any of the names that can easily be created by extending the naming pattern (unvigintillion, duovigintillion, duoquinquagintillion, etc.)

All of the dictionaries included googol and googolplex, generally crediting it to the Kasner and Newman book and to Kasners' nephew. None include any higher names in the googol family (googolplexplex, etc.) The Shorter Oxford English Dictionary comments that googol and googolplex are "not in formal mathematical use."

• Vigintillion is used by H. P. Lovecraft in a Cthulu story.

Dictionaries cited:
AHD4: American Heritage Dictionary, 4th edition, at http://www.bartleby.com/61
ShorterOED3-1993: Shorter Oxford English Dictionary, 3rd edition, 1993, Oxford: Clarendon Press
RHD2-1987: The Random House Dictionary, 2nd Unabridged Edition, 1987, Random House
W3-1993: Webster's Third New International Dictionary, Unabridged, 1993, Merriam-Webster
OED2: Oxford English Dictionary, 2nd edition, Oxford: Oxford University Press ; (and addendums since publication in 1989)
OEDnew: Oxford English Dictionary, New Edition, Oxford: Oxford University Press ; at http://www.oed.com (subscription required)
Dcom: Dictionary.com

√ means the word is included in the dictionary
× means the word is not included in the dictionary

Usage of names of large numbers

Some large numbers have real referents in human experience. Their names are real words, encountered in many contexts. For example, today, Google News shows 78,600 hits on "billion," starting with "Turkey Repays $1.6 Billion In Foreign Debt." It shows 9870 hits on "trillion," and 56 on "quadrillion:" "The US Department of Energy reports that in 2002, the United States economy consumed 97.6 quadrillion btus (quad btus)."

References to names of quantities larger than a quadrillion, however, are rare, and increasingly artificial; they tend to be limited to discussions of names of numbers, or mathematical concepts. For example, the first hit on "quintillion" is about a man who is trying to preserve the Etsako language by codifying it, and "went as far as providing numerals from one to quintillion." "Septillion" appears—as the name of a racing yacht.

It can be argued that a number such as a "trigintillion" has no existence in the physical world. There simply is not a trigintillion of anything, and no practical need for such a name.

Nevertheless, large numbers have an intellectual fascination and are of mathematical interest. Giving them names one of the ways in which people try to conceptualize and understand them.

In The Sand Reckoner, Archimedes estimated the number of grains of sand that would be required to fill the known universe. To do this, he called a myriad myriad (10⁸) a "first number;" a myriad myriad first numbers as "second numbers" (10¹⁶), and so on up to "eighth numbers" (10⁶⁴). He concluded that it would take less than "one thousand myriad myriad eighth numbers" grains of sand to pack the universe solid with sand.

Since then, many others have engaged in the pursuit of conceptualizing and naming numbers that really have no existence outside of the imagination. One motivation for such a pursuit is that attributed to the inventor of the word googol, who was certain that any finite number "had to have a name." Another possible motivation is competition between students in computer programming courses, where a common exercise is that of writing a program to output numbers in the form of English words.

Names of numbers large than a quadrillion, even if found in dictionaries, have a tenuous existence. Just as one can debate whether "floccinaucinihilipilification" is really an English word—it is in the Oxford English Dictionary, but no other—it is questionable how real the word "trigintillion" is. "Trigintillion" is only encountered in definitions, lists of names of large numbers, and "Sand Reckoner"-like discourses on the meaning of very large numbers.

Even well-established names like "sextillion" are rarely used, even in those contexts where they have a real meaning—science, astronomy, and engineering. In science, since the 1800s, numbers have been written using the familiar "scientific notation," in which powers of ten are expressed as a ten with a numeric superscript, e.g. "The X-ray emission of the radio galaxy is 1.3 × 10⁴⁵ ergs." When a number such as 10⁴⁵ needs to be referred to in words, it is simply read out: "ten to the forty-fifth." This is just as easy to say, easier to understand, and less ambiguous than "quattuordecillion" (which means something different to American and British audiences—assuming that there are any listeners who understand this number without consulting a dictionary). When a number represents a measurement rather than a count, SI prefixes are used; one says "femtosecond," not "one quadrillionth of a second." In some cases, specialized very large or large units are used, such as the astronomer's parsec and light year.

It should be noted, too, that most names proposed for large numbers belong to systematic schemes which are extensible. Thus, many names for large numbers are simply the result of following a naming system to its logical conclusion—or extending it further. Glancing at the table for the Googol family, it is clear what the value of a "Googolquattuordeciplex" would be if there were such a word, but that does not mean that such a word exists, nor that there is any value in coining it.

Here we present some names that have been given to large numbers, and the context and authority for the names. These numbers are almost pure mathematical abstractions, not physical realities. The names for such numbers are very rarely used. They may have a claim staked out for them in reference books, but they remain more in the nature of curiosities, trivia, or mathematical recreation than genuine working English vocabulary.

Chuquet and the origins of the "standard dictionary numbers"

Nicolas Chuquet's book Triparty en la science des nombres was not published during his lifetime, but most of it was copied by Estienne de la Roche for a portion of his 1520 book, Larismetique. Chuquet's book contains a passage in which he shows a large number marked off into groups of six digits, with the comment:

Ou qui veult le premier point peult signiffier million Le second point byllion Le tiers poit tryllion Le quart quadrillion Le cinq^e quyllion Le six^e sixlion Le sept.^e septyllion Le huyt^e ottyllion Le neuf^e nonyllion et ainsi des ault'^s se plus oultre on vouloit preceder

(Or if you prefer the first mark can signify million, the second mark byllion, the third mark tryllion, the fourth quadrillion, the fifth quyillion, the sixth sixlion, the seventh septyllion, the eighth ottyllion, the ninth nonyllion and so on with others as far as you wish to go).

Because of this passage, Chuquet is sometimes credited with "inventing" the names million, billion, trillion, quadrillion, and so forth. This is an oversimplification.

• "million" was certainly not invented by Chuquet. "milion" is an Old French word thought to derive from Old Italian "milione," an intensification of "mille," a thousand. That is, "a million" is a "big thousand," much as 1728 is a "great gross."
• The words "bymillions" and "trimillions" were first recorded in 1475 in a work by Jehan Adam.
• From the way in which Adam and Chuquet use the words, it can be inferred that they were recording usage rather than inventing it. One obvious possibility is that words similar to "billion" and "trillion" were already in use and well-known, but that Chuquet, an expert in exponentiation, did extend the naming scheme and invent the names for the higher powers.
• Notice that Chuquet's names are only similar to, not identical to the modern ones.

Both Adam and Chuquet applied the names to powers of a million; that is, a bimillion (Adam) or byllion (Chuquet) was 10¹², and a trimillion (Adam) or tryllion (Chuquet) was 10¹⁸.

The Googol family

The googol and googolplex were introduced in Kasner and Newman's 1940 book, Mathematics and the Imagination, thus:

Words of wisdom are spoken by children at least as often as by scientists. The name "googol" was invented by a child (Dr. Kasner's nine-year-old nephew) who was asked to think up a name for a very big number, namely 1 with a hundred zeroes after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested "googol" he gave a name for a still larger number: "Googolplex." A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It as first suggested that a googolplex should be 1, followed by writing zeros until you got tired. This is a description of what would actually happen if one actually tried to write a googolplex, but different people get tired at different times and it would never do to have Carnera a better mathematician than Dr. Einstein, simply because he had more endurance. The googolplex is, then, a specific finite number, with so many zeros after the 1 that the number of zeros is a googol.

Value	Name	Authority
10100	Googol	Kasner and Newman, dictionaries (see above)
1010100	Googolplex	Kasner and Newman, dictionaries (see above)
101010100	Googolplexplex or Googolduplex
10101010100	Googolplexplexplex or Googoltriplex
1010101010100	Googolplexplexplexplex

Extensions of the standard dictionary numbers

This table illustrates several systems for naming large numbers, and shows how they can be extended past decillion.

Traditional British usage used new names for each power of one million. It was adapted from French usage, and is similar to the system that was documented or invented by Chuquet.

Traditional American usage (which, oddly enough, was also adapted from French usage but at a later date) uses new names for each power of one thousand, with a "billion" being 10⁹, a "trillion" being 10¹², and so forth.

As early as 1929 Fowler's Modern English Usage recommended the use of the American nomenclature, and in 1974 the British Government adopted it for official British reports and statistics.

Traditional French usage has varied; in 1948, France, which had been using the American-style terminology, reverted to the Chuquet-style nomenclature.

The term milliard is unambiguous and always means 10⁹. It is almost never seen in American usage, sometimes in British usage, and frequently in European usage. The term is sometimes attributed to a French mathematician named Pelletier circa 1550, but the Oxford English Dictionary states that the term derives from post-Classical latin term milliartum, which became milliare and then milliart and finally to our modern term.

For additional details, see: billion

Value	USA	Traditional British	Traditional European (Pelletier)
103	Thousand	Thousand	Thousand
106	Million	Million	Million
109	Billion	Thousand million	Milliard
1012	Trillion	Billion	Billion
1015	Quadrillion	Thousand billion	Billiard
1018	Quintillion	Trillion	Trillion
1021	Sextillion	Thousand trillion	Trilliard
1024	Septillion	Quadrillion	Quadrillion
1027	Octillion	Thousand quadrillion	Quadrilliard
1030	Nonillion	Quintillion	Quintillion
1033	Decillion	Thousand quintillion	Quintilliard
1036	Undecillion	Sextillion	Sextillion
1039	Duodecillion	Thousand sextillion	Sextilliard
1042	Tredecillion	Septillion	Septillion
1045	Quattuordecillion	Thousand septillion	Septilliard
1048	Quindecillion	Octillion	Octillion
1051	Sexdecillion	Thousand octillion	Octilliard
1054	Septendecillion	Nonillion	Nonillion
1057	Octodecillion	Thousand nonillion	Nonilliard
1060	Novemdecillion	Decillion	Decillion
1063	Vigintillion	Thousand decillion	Decilliard
1066	Unvigintillion	Undecillion	Undecillion
1069	Duovigintillion	Thousand undecillion	Undecilliard
1072	Trevigintillion	Duodecillion	Duodecillion
1075	Quattuorvigintillion	Thousand duodecillion	Duodecilliard
1078	Quinvigintillion	Tredecillion	Tredecillion
1081	Sexvigintillion	Thousand tredecillion	Tredecilliard
1084	Septenvigintillion	Quattuordecillion	Quattuordecillion
1087	Octovigintillion	Thousand quattuordecillion	Quattuordecilliard
1090	Novemvigintillion	Quindecillion	Quindecillion
1093	Trigintillion	Thousand quindecillion	Quindecilliard
1096	Untrigintillion	Sexdecillion	Sexdecillion
1099	Duotrigintillion	Thousand sexdecillion	Sexdecilliard
10102	Tretrigintillion	Septendecillion	Septendecillion
10105	Quattuortrigintillion	Thousand septendecillion	Septendecilliard
10108	Quintrigintillion	Octodecillion	Octodecillion
10111	Sextrigintillion	Thousand octodecillion	Octodecilliard
10114	Septentrigintillion	Novemdecillion	Novemdecillion
10117	Octotrigintillion	Thousand novemdecillion	Novemdecilliard
10120	Novemtrigintillion	Vigintillion	Vigintillion
10123	Quadragintillion	Thousand vigintillion	Vigintilliard
10126	Unquadragintillion	Unvigintillion	Unvigintillion
10129	Duoquadragintillion	Thousand unvigintillion	Unvigintilliard
10132	Trequadragintillion	Duovigintillion	Duovigintillion
10135	Quattuorquadragintillion	Thousand duovigintillion	Duovigintilliard
10138	Quinquadragintillion	Trevigintillion	Trevigintillion
10141	Sexquadragintillion	Thousand trevigintillion	Trevigintilliard
10144	Septenquadragintillion	Quattuorvigintillion	Quattuorvigintillion
10147	Octoquadragintillion	Thousand quattuorvigintillion	Quattuorvigintilliard
10150	Novemquadragintillion	Quinvigintillion	Quinvigintillion
10153	Quinquagintillion	Thousand quinvigintillion	Quinvigintilliard
10156	Unquinquagintillion	Sexvigintillion	Sexvigintillion
10159	Duoquinquagintillion	Thousand sexvigintillion	Sexvigintilliard
10162	Trequinquagintillion	Septenvigintillion	Septenvigintillion
10165	Quattuorquinquagintillion	Thousand septenvigintillion	Septenvigintilliard
10168	Quinquinquagintillion	Octovigintillion	Octovigintillion
10171	Sexquinquagintillion	Thousand octovigintillion	Octovigintilliard
10174	Septenquinquagintillion	Novemvigintillion	Novemvigintillion
10177	Octoquinquagintillion	Thousand novemvigintillion	Novemvigintilliard
10180	Novemquinquagintillion	Trigintillion	Trigintillion
10183	Sexagintillion	Thousand trigintillion	Trigintilliard
...	...	...	...
10213	Septuagintillion	Thousand quintrigintillion	Quintrigintilliard
...	...	...	...
10240	Novemseptuagintillion	Quadragintillion	Quadragintillion
10243	Octogintillion	Thousand quadragintillion	Quadragintilliard
...	...	...	...
10273	Nonagintillion	Thousand quinquadragintillion	Quinquadragintilliard
...	...	...	...
10300	Novemnonagintillion	Quinquagintillion	Quinquagintillion
10303	Centillion	Thousand quinquagintillion	Quinquagintilliard
...	...	...	...
10360		Sexagintillion	Sexagintillion
10363		Thousand sexagintillion	Sexagintilliard
...	...	...	...
10420		Septuagintillion	Septuagintillion
10423		Thousand septuagintillion	Septuagintilliard
...	...	...	...
10480		Octogintillion	Octogintillion
10483		Thousand octogintillion	Octogintilliard
...	...	...	...
10540		Nonagintillion	Nonagintillion
10543		Thousand nonagintillion	Nonagintilliard
...	...	...	...
10600		Centillion	Centillion
10603		Thousand centillion	Centilliard
...	...	...	...

Other systematic names of large numbers

This table contains a list of numbers that extend to very large sums. Many of these entries should be considered trivia or curiosities.

Value	Extended American (Chuquet)	Extended European (Pelletier)	Extended Myriadic (Knuth)	Extended Myriadic (Knuth-Pelletier)
0	Zero	Zero	Zero	Zero
101	One	One	One	One
103	Thousand	Thousand	Thousand	Thousand
104	Ten thousand	Ten thousand	Myriad	Myriad
106	Million	Million	Hundred myriad	Hundred myriad
108	Hundred million	Hundred million	Myllion	Myllion
109	Billion	Milliard	Ten myllion	Ten myllion
1012	Trillion	Billion	Myriad myllion	Myriad myllion
1015	Quadrillion	Billiard	Thousand myriad myllion	Thousand myriad myllion
1016	Ten quadrillion	Ten billiard	Byllion	Mylliard
1024	Septillion	Quadrillion	Myllion byllion	Myllion mylliard
1032	Hundred nonillion	Hundred quintillion	Tryllion	Byllion
1033	Decillion	Quintilliard	Ten tryllion	Ten byllion
1060	Novemdecillion	Decillion	Myriad myllion byllion tryllion	Myriad myllion mylliard byllion
1063	Vigintillion	Decilliard	Thousand myriad myllion byllion tryllion	Thousand myriad myllion mylliard byllion
1064	Ten vigintillion	Ten decilliard	Quadryllion	Bylliard
10303	Centillion	Quinquagintilliard	Thousand myriad myllion tryllion sextyllion	Thousand myriad myllion byllion trylliard
10600	Novenonacentillion?	Centillion	Myllion byllion quadryllion septyllion	Myllion mylliard trylliard quadryllion
10603	Duecentillion	Centilliard	Thousand myllion byllion quadryllion septyllion	Thousand myllion mylliard trylliard quadryllion
103003	Millillion	Pentacentilliard?	Thousand myllion byllion tryllion quintyllion sextyllion septyllion nonyllion	?
106000	Novenonaennecentumillillion?	Millillion	Byllion tryllion sextyllion septyllion octyllion decyllion	?
106003	Duemillillion?	Millilliard	Thousand byllion tryllion sextyllion septyllion octyllion decyllion	?
1030,003	Myrillion	Pentamillilliard?	Thousand byllion tryllion sextyllion octyllion decyllion undecyllion duodecyllion	?
1060,000	Novenonaennecentupentamillimyrillion?	Myrillion	Tryllion quadryllion septyllion nonyllion undecyllion duodecyllion tredecyllion	?
1060,003	Duemyrillion?	Myrilliard	Thousand tryllion quadryllion septyllion nonyllion undecyllion duodecyllion tredecyllion	?
10300,003	?	?	?	?
10600,000	?	?	?	?
10600,003	?	?	?	?
103,000,003	Micrillion	?	?	?
103,000,000,003	Nanillion	?	?	?
103*1012+3	Picillion	?	?	?
103*1015+3	Femtillion	?	?	?
103*1018+3	Attillion	?	?	?
103*1021+3	Zeptillion	?	?	?
103*1024+3	Yoctillion	?	?	?
103*1027+3	Xonillion	?	?	?
103*1030+3	Dekillion Vecillion Contillion	?	?	?
103*1033+3	Mecillion	?	?	?
103*1036+3	Duecillion	?	?	?
103*1039+3	Trecillion	?	?	?
103*1042+3	Tetrecillion	?	?	?
103*1045+3	Pentecillion	?	?	?
103*1048+3	Hexecillion	?	?	?
103*1051+3	Heptecillion	?	?	?
103*1054+3	Octecillion	?	?	?
103*1057+3	Ennecillion	?	?	?
103*1060+3	Icocillion Ducontillion	?	?	?
103*1090+3	Triacontillion	?	?	?
103*10120+3	Tetracontillion	?	?	?
103*10150+3	Pentacontillion	?	?	?
103*10180+3	Hexacontillion	?	?	?
103*10210+3	Heptacontillion	?	?	?
103*10240+3	Octacontillion	?	?	?
103*10270+3	Ennacontillion	?	?	?
103*10300+3	Hectillion Icocontillion	?	?	?
103*103000+3	Killillion Onillion	?	?	?
103*103,000,000+3	Megillion	?	?	?
103*103,000,000,000+3	Gigillion	?	?	?
103*103*1012+3	Terillion	?	?	?
103*103*1015+3	Petillion	?	?	?
103*103*1018+3	Exillion	?	?	?
103*103*1021+3	Zettillion	?	?	?
103*103*1024+3	Yottillion	?	?	?
103*103*1027+3	Xennillion	?	?	?
103*103*1030+3	Vekillion Teenillion	?	?	?
103*103*1033+3	Mekillion	?	?	?
103*103*1036+3	Duekillion	?	?	?
103*103*1039+3	Trekillion	?	?	?
103*103*1042+3	Tetrekillion	?	?	?
103*103*1045+3	Pentekillion	?	?	?
103*103*1048+3	Hexekillion	?	?	?
103*103*1051+3	Heptekillion	?	?	?
103*103*1054+3	Octekillion	?	?	?
103*103*1057+3	Ennekillion	?	?	?
103*103*1060+3	Icokillion Twentillion	?	?	?
103*103*1090+3	Thirtillion	?	?	?
103*103*10120+3	Fortillion	?	?	?
103*103*10150+3	Fiftillion	?	?	?
103*103*10180+3	Sixtillion	?	?	?
103*103*10210+3	Seventillion	?	?	?
103*103*10240+3	Eightillion	?	?	?
103*103*10270+3	Nintillion	?	?	?
103*103*10300+3	Hundrillion	?	?	?
103*103*103000+3	Thousillion	?	?	?
103*103*1030,000+3	Myriaillion Manillion	?	?	?
103*103*10300,000+3	Lakhillion	?	?	?
103*103*103,000,000+3	?	?	?	?
103*103*1030,00,000+3	Crorillion	?	?	?
103*103*10300,000,000+3	Awkillion	?	?	?
106*103*10300,000,000	?	Awkillion	?	?
?106*103*10300,000,000+3?	?	?Awkilliard?	?	?
...	...	...	...	...

[1] [2] [3] [4] [5] Commercial Product using Yoctillion

See Also

• List of numbers
• Large numbers
• Chuquet
• Pelletier
• Knuth

References

• Kasner, Edward and James Newman, Mathematics and the Imagination, 1940, Simon and Schuster, New York.
• Weisstein, Math World, Wolfram Research, http://mathworld.wolfram.com