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Sextillion

The "standard dictionary numbers"

Throughout this article, exponential or scientific 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 larger 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 and modern British value ("short scale")	Traditional British value ("long scale")	Authorities	Google hits
million	106	106	√ AHD4, √ COD, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993	54,900,000 Pages 6,880,000 Articles
milliard		109	√ AHD4, √ OED2	24,300 English pages 466,700 other pages 41,000 Articles
billion	109	1012	√ AHD4, √ COD, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993	12,700,000 English pages (mostly using 109) 3,000,000 other pages 2,200,000 Articles
trillion	1012	1018	√ AHD4, √ COD, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993	1,460,000 Pages 303,000 Articles
quadrillion	1015	1024	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993	63,200 Pages 52,800 Articles
quintillion	1018	1030	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993	15,300 Pages 42,900 Articles
sextillion	1021	1036	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993	6,260 Pages 38,500 Articles
septillion	1024	1042	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993	3,460 Pages 37,800 Articles
octillion	1027	1048	√ AHD4, √ OED2, √ OEDnew, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993	3,440 Pages 39,700 Articles
nonillion	1030	1054	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993	1,980 Pages 715 Articles
decillion	1033	1060	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993	4,940 Pages 783 Articles
undecillion	1036	1066	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993	854 Pages 294 Articles
duodecillion	1039	1072	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993	1250 Pages 249 Articles
tredecillion	1042	1078	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993	885 Pages 182 Articles
quattuordecillion	1045	1084	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993	830 Pages 154 Articles
quindecillion	1048	1090	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993	686 Pages 151 Articles
sexdecillion	1051	1096	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993	759 Pages 145 Articles
septendecillion	1054	10102	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993	699 Pages 138 Articles
octodecillion	1057	10108	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993	863 Pages 157 Articles
novemdecillion	1060	10114	√ AHD4, √ RHD2-1987, × ShorterOED3-1993, √ W3-1993	941 Pages 182 Articles
vigintillion	1063	10120	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993	1550 Pages 410 Articles
googol	10100	10100	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993	82,500 Pages 10,200 Articles
centillion	10303	10600	√ AHD4, √ OED2	8560 Pages 25 Articles
googolplex	10googol	10googol	√ AHD4, √ OED2, √ RHD2-1987, √ ShorterOED3-1993, √ W3-1993	28,100 Pages 14,400 Articles

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
COD: Cambridge Online Dictionaries, Cambridge, UK: Cambridge University Press ; at http://dictionary.cambridge.org
OED2: Oxford English Dictionary, 2nd edition, Oxford, UK: Oxford University Press ; (and addendums since publication in 1989)
OEDnew: Oxford English Dictionary, New Edition, Oxford, UK: Oxford University Press ; at http://www.oed.com (subscription required)
RHD2-1987: The Random House Dictionary, 2nd Unabridged Edition, 1987, Random House
ShorterOED3-1993: Shorter Oxford English Dictionary, 3rd edition, 1993, Oxford: Clarendon Press
W3-1993: Webster's Third New International Dictionary, Unabridged, 1993, Merriam-Webster
Dcom: Dictionary.com

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

"Google hits" means the number of hits reported by Google when searching the entire web and the DejaNews USENET archives as of June 4, 2004.

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, on one day in 2004, Google News showed 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 is 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 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).

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.

Adam and Chuquet used the "long scale" of powers of a million; that is, a bimillion (Adam) 10¹², and a trimillion was 10¹⁸.

The Googol family

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

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 was 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)
10googol = <math>\,\!10^{10^{100}}<math>	Googolplex	Kasner and Newman, dictionaries (see above)
10googolplex = <math>\,\!10^{10^{10^{100}}}<math>	Googolplexplex or Googolduplex
10googolduplex = <math>\,\!10^{10^{10^{10^{100}}}}<math>	Googolplexplexplex or Googoltriplex
10googoltriplex = <math>\,\!10^{10^{10^{10^{10^{100}}}}}<math>	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 assigned new names for each power of one million (the long scale). 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), and modern British usage, assigns new names for each power of one thousand (the short scale. Thus, a "billion" is 10⁹, a "trillion" is 10¹², and so forth.

Traditional French usage has varied; in 1948, France, which had been using the short scale, reverted to the long scale.

The term milliard is unambiguous and always means 10⁹. It is almost never seen in American usage, rarely in British usage, and frequently in European usage. The term is sometimes attributed to a French mathematician named Jacques Pelletier du Mans 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.

With regard to names ending in -illiard, milliard is certainly in widespread use, but the degree of actual use of the larger terms is questionable. For example, as of 2004, Google searches on French-language pages for "trillion," "trilliard," "quadrillion," "quadrilliard," and "quintillion" return, respectively, 6630, 102, 312, 7, and 127 hits, respectively.

For additional details, see: billion and long scale.

Value	USA and Modern British ("short scale")	Traditional British ("long scale")	Traditional European (Pelletier) ("long scale")
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
...	...	...	...

For non-standard conventions that assign regular names to even larger numbers, see Other names of large numbers.

See Also

• List of numbers
• Large numbers
• Nicolas Chuquet
• Indian numbering system
• Jacques Pelletier du Mans
• Knuth
• Other names of large numbers