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Archive 1Archive 2

Extensions of the standard dictionary numbers

{{Refimprovesect|date=June 2006}} {{Original research|section|date=January 2007}}

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): 1,000,000 = 1 million; 1,000,0002 = 1 billion; 1,000,0003 = 1 trillion; and so on. 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 1000 × 10002 = 109; a trillion is 1000 × 10003 = 1012; and so forth. Due to its dominance in the financial world (and by the US-dollar) this was adopted for official United Nations documents.

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 Peletier du Mans circa 1550 (for this reason, the long scale is also known as the Chuquet-Peletier system), but the Oxford English Dictionary states that the term derives from post-Classical Latin term milliartum, which became milliare and then milliart and finally our modern term.

With regard to names ending in -illiard for numbers 106·n+3, milliard is certainly in widespread use in languages other than English, 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, quadrillion, and quintillion return 6630, 312, and 127 hits respectively, whilst searches for trilliard and quadrilliard return only 102 and 7 hits respectively. However, one has to take into account that these large numbers are not often needed and that scientists almost always use scientific notation. In German the terms "Milliarde", "Billiarde" etc. are out of question.

The naming procedure for large numbers is based on taking the number n occurring in 103n+3 (short scale) or 106n (long scale) and concatenating Latin roots for its units, tens, and hundreds place, together with the suffix -illion. In this way, numbers up to 103·999+3 = 103000 (short scale) or 106·999 = 105994 (long scale) may be named. The choice of roots and the concatenation procedure is that of the standard dictionary numbers if n is 20 or smaller, and, for larger n (between 21 and 999), is due to John Horton Conway and Richard Guy. Since the system of using Latin prefixes will become ambiguous for numbers with exponents of a size which the Romans rarely counted to, like 106,000,258, Conway and Guy have also proposed a consistent set of conventions which permit, in principle, the extension of this system to provide English names for any integer whatsoever.[1]

Names of reciprocals of large numbers do not need to be listed here, because they are regularly formed by adding -th, e.g. quattuordecillionth, centillionth, etc.

For additional details, see Billion (disambiguation) and long and short scales.

Base -illion (short scale) Value USA and Modern British
(short scale)
Traditional British
(long scale)
Traditional European (Peletier)
(long scale)
1 106 Million Million Million
2 109 Billion Thousand million Milliard
3 1012 Trillion Billion Billion
4 1015 Quadrillion Thousand billion Billiard
5 1018 Quintillion Trillion Trillion
6 1021 Sextillion Thousand trillion Trilliard
7 1024 Septillion Quadrillion Quadrillion
8 1027 Octillion Thousand quadrillion Quadrilliard
9 1030 Nonillion Quintillion Quintillion
10 1033 Decillion Thousand quintillion Quintilliard
11 1036 Undecillion Sextillion Sextillion
12 1039 Duodecillion Thousand sextillion Sextilliard
13 1042 Tredecillion Septillion Septillion
14 1045 Quattuordecillion Thousand septillion Septilliard
15 1048 Quindecillion Octillion Octillion
16 1051 Sexdecillion Thousand octillion Octilliard
17 1054 Septendecillion Nonillion Nonillion
18 1057 Octodecillion Thousand nonillion Nonilliard
19 1060 Novemdecillion Decillion Decillion
20 1063 Vigintillion Thousand decillion Decilliard
21 1066 Unvigintillion Undecillion Undecillion
22 1069 Duovigintillion Thousand undecillion Undecilliard
23 1072 Tresvigintillion Duodecillion Duodecillion
24 1075 Quattuorvigintillion Thousand duodecillion Duodecilliard
25 1078 Quinquavigintillion Tredecillion Tredecillion
26 1081 Sesvigintillion Thousand tredecillion Tredecilliard
27 1084 Septemvigintillion Quattuordecillion Quattuordecillion
28 1087 Octovigintillion Thousand quattuordecillion Quattuordecilliard
29 1090 Novemvigintillion Quindecillion Quindecillion
30 1093 Trigintillion Thousand quindecillion Quindecilliard
31 1096 Untrigintillion Sexdecillion Sexdecillion
32 1099 Duotrigintillion Thousand sexdecillion Sexdecilliard
33 10102 Trestrigintillion Septendecillion Septendecillion
34 10105 Quattuortrigintillion Thousand septendecillion Septendecilliard
35 10108 Quinquatrigintillion Octodecillion Octodecillion
36 10111 Sestrigintillion Thousand octodecillion Octodecilliard
37 10114 Septentrigintillion Novemdecillion Novemdecillion
38 10117 Octotrigintillion Thousand novemdecillion Novemdecilliard
39 10120 Noventrigintillion Vigintillion Vigintillion
40 10123 Quadragintillion[2] Thousand vigintillion Vigintilliard
50 10153 Quinquagintillion Thousand quinquavigintillion Quinquavigintilliard
60 10183 Sexagintillion Thousand trigintillion Trigintilliard
70 10213 Septuagintillion Thousand quinquatrigintillion Quinquatrigintilliard
80 10243 Octogintillion Thousand quadragintillion Quadragintilliard
90 10273 Nonagintillion Thousand quinquaquadragintillion Quinquaquadragintilliard
100 10303 Centillion Thousand quinquagintillion Quinquagintilliard
101 10306 Uncentillion Unquinquagintillion Unquinquagintillion
102 10309 Duocentillion Thousand unquinquagintillion Unquinquagintilliard
103 10312 Trescentillion Duoquinquagintillion Duoquinquagintillion
110 10333 Decicentillion Thousand quinquaquinquagintillion Quinquaquinquagintilliard
121 10366 Unviginticentillion Unsexagintillion Unsexagintillion
130 10393 Trigintacentillion Thousand quinquasexagintillion Quinquasexagintilliard
140 10423 Quadragintacentillion Thousand septuagintillion Septuagintilliard
150 10453 Quinquagintacentillion Thousand quinquaseptuagintillion Quinquaseptuagintilliard
160 10483 Sexagintacentillion Thousand octogintillion Octogintilliard
170 10513 Septuagintacentillion Thousand quinquaoctogintillion Quinquaoctogintilliard
180 10543 Octogintacentillion Thousand nonagintillion Nonagintilliard
190 10573 Nonagintacentillion Thousand quinquanonagintillion Quinquanonagintilliard
200 10603 Ducentillion Thousand centillion Centilliard
300 10903 Trecentillion Thousand quinquagintacentillion Quinquagintacentilliard
400 101203 Quadringentillion Thousand ducentillion Ducentilliard
500 101503 Quingentillion Thousand quinquagintaducentillion Quinquagintaducentilliard
600 101803 Sescentillion Thousand trecentillion Trecentilliard
700 102103 Septingentillion Thousand quinquagintatrecentillion Quinquagintatrecentilliard
800 102403 Octingentillion Thousand quadringentillion Quadringentilliard
900 102703 Nongentillion Thousand quinquagintaquadringentillion Quinquagintaquadringentilliard
1000 103003   Thousand quingentillion Quingentilliard
Value USA and Modern British
(short scale)
Traditional British
(long scale)
Traditional European (Peletier)
(long scale)
10100 Googol (Ten duotrigintillion) Googol (Ten thousand sexdecillion) Googol (Ten sexdecilliard)
Googolplex Googolplex Googolplex

References

  1. ^ Cite error: The named reference a was invoked but never defined (see the help page).
  2. ^ Often misspelled quardragintillion.

What did Chuquet really propose?

Several Web pages make a reference to a passage in Chuquet's book in which he shows a large number marked off into groups of six digits and comments:

Ou qui veult le premier point peult signiffier million Le second point byllion Le tiers poit tryllion Le quart quadrillion Le cinqe quyllion Le sixe sixlion Le sept.e septyllion Le huyte ottyllion Le neufe 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).

This clearly refers to names in steps of powers of six. But *Robert Munafo's article quotes a different passage,

Au lieu de dire mille milliers, on dira million, au lieu de dire mille millions, on dira byllion, etc..., et tryllion, quadrilion ... octylion, nonyllion, et ainsi des autres si plus oultre on voulait proceder. French: "Instead of saying one thousand thousand, one may say million; instead of saying one thousand million, one may say billion, and trillion, quadrillion, ... octillion, nonillion, and others as well, as far as you wish to go."

and comments

These number names were adopted throughout Europe during the next century (with minor spelling changes for each language). Chuquet intended the names to represent powers of 1000 as the quote above clearly shows.

So, it's not at all clear to me what the Chuquet system really was. — Preceding unsigned comment added by Dpbsmith (talkcontribs) 13:36, 5 June 2004 (UTC)

Usage in science

Shouldn't this article have a bit of text about the fact that none of these words are used in science because of their ambiguous nature? — Preceding unsigned comment added by 217.122.115.98 (talk) 16:49, 11 August 2005 (UTC)

Other names of large numbers

I have listed other names of large numbers on AfD (Wikipedia:Articles_for_deletion/Other_names_of_large_numbers), people watching this page might want to comment on it. — Preceding unsigned comment added by Ruud Koot (talkcontribs) 03:09, 12 February 2006 (UTC)

Quadrillion

Just thought I would mention I found this article when I actually needed to use the word for 1015 and did not know it's word[1].

Thanks for the informative article. — Preceding unsigned comment added by H (talkcontribs) 16:48, 1 July 2006 (UTC)

A suggestion of large number names

Why use centillion, not hectillion, for 10303? In SI prefix, "centi-" is 10−2, and "hecto-" is 102, and the number is "100-illion", not "0.01-illion"!!! Thus should be hectillion, not centillion.

A suggestion of larger number names is: (in American scale, or short scale)

hectillion = 10303

kilillion = 103003

megillion = 103×106+3

gigillion = 103×109+3

terillion = 103×1012+3

petillion = 103×1015+3

exillion = 103×1018+3

zettillion = 103×1021+3

yottillion = 103×1024+3

xonillion = 103×1027+3

wecillion = 103×1030+3

— Preceding unsigned comment added by 101.8.178.137 (talk) 15:32, 11 June 2018 (UTC)

Please add Googolplexian

10^10^10^100Googolplex‹∞› — Preceding unsigned comment added by 2601:CD:C882:8D20:4008:B107:4C6A:293C (talk) 17:18, 17 June 2023 (UTC)

nomenclature for numbers very large indices base 10

My son (Charlie C.) asked about what a number would be called if it had a quadrillion zeros.

He came up with a prefix dind-

So dindquadrillion.

Prefix dind meaning "deco index"

Is this type of number already succintly named? If so, what nomenclature do people use? 2001:8003:ED68:D500:5C75:FE6A:9568:ADDC (talk) 21:48, 2 September 2023 (UTC)

I don't think we have or need common names for such numbers, simply because there aren't that many of anything. For example, to describe the number of atoms in the universe, we only need 80 zeros. Even there, 1080 seems a lot easier to understand than obscure wording such as a hundred quinvigintillion. Certes (talk) 22:56, 2 September 2023 (UTC)

Million,Milliard,Billion,Trillion,Quadrillion,Quintillion had a Un,Duo,Tre,Quattuor and Quin

Well here it is:

Unmillion Unmilliard Unbillion Untrillion Unquadrillion Unquintillion

Duomillion Duomilliard Duobillion Duotrillion Duoquadrillion Duoquintillion

Tremillion Tremilliard Trebillion Tretrillion Trequadrillion Trequintillion

Quattuormillion Quattuormilliard Quattuorbillion Quattuortrillion Quattuorquadrillion Quattuorquintillion

Quinmillion Quinmilliard Quinbillion Quintrillion Quinquadrillion Quinquintillion

That's all. — Preceding unsigned comment added by 178.88.205.90 (talk) 20:17, 6 September 2023 (UTC)

Suggestions of numbers

Hectillion = 103,078 Unhectillion = 103,081 Duohectillion = 103,084 Trehectillion = 103,087 Quattuorhectillion = 103,090 Quinhectillion = 103,093 Sexhectillion = 103,096 Septenhectillion = 103,099 Octohectillion = 103,102 Novemhectillion = 103,105 213.211.86.128 (talk) 10:23, 19 September 2023 (UTC)

Thank you, but this article is only for common names used widely in reliable sources. Wikipedia does not publish original research such as inventing new names. Certes (talk) 12:08, 19 September 2023 (UTC)

Maximusquintillion

It's 101,000,000,000,000,000,000 or 101018 — Preceding unsigned comment added by 2.132.8.107 (talk) 14:01, 25 November 2023 (UTC)

Maximunssextillion

Say the number of maximunssextillion Luccasantana (talk) 22:57, 2 February 2024 (UTC)

That's not a real number. Black Yoshi (Yoshi! | Yoshi's Eggs) 22:58, 2 February 2024 (UTC)

What is the name of the 1089 digit emirp?

There is a reversed prime number (emirp) defined by Jens Kruse Andersen from Denmark (http://primerecords.dk) that has 1089 digits. I don't seem to find a name for it in Wikipedia. 115.64.52.116 (talk) 07:04, 16 March 2024 (UTC)