Talk:Names of large numbers/Archive 2

Archive 1

Archive 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 10^6·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 10^3·999+3 = 10³⁰⁰⁰ (short scale) or 10^6·999 = 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 10^6,000,258, 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.

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	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)
$10^{10^{100}}\,\!$	Googolplex	Googolplex	Googolplex

References

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 (talk • contribs) 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 (talk • contribs) 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 (talk • contribs) 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 = 10^3×106+3

gigillion = 10^3×109+3

terillion = 10^3×1012+3

petillion = 10^3×1015+3

exillion = 10^3×1018+3

zettillion = 10^3×1021+3

yottillion = 10^3×1024+3

xonillion = 10^3×1027+3

wecillion = 10^3×1030+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 = 10^3,078 Unhectillion = 10^3,081 Duohectillion = 10^3,084 Trehectillion = 10^3,087 Quattuorhectillion = 10^3,090 Quinhectillion = 10^3,093 Sexhectillion = 10^3,096 Septenhectillion = 10^3,099 Octohectillion = 10^3,102 Novemhectillion = 10^3,105 213.211.86.128 (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 10^{1,000,000,000,000,000,000} 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)

HM and UM

The table for googol and googolplex has UM as an authority, but it hasn't been mentioned before and has no link. I believe it's supposed to represent the HM reference, but it doesn't say that. 130.226.139.26 (talk) 07:24, 22 April 2024 (UTC)

Fixed. Black Yoshi (Yoshi! | Yoshi's Eggs) 12:20, 22 April 2024 (UTC)

Base -illion orders of magnitude

Does this make 1,000 the zeroth base -illion, and 1 the negative first base -illion? 2601:1C0:847C:50C0:A54D:85AC:91BC:7681 (talk) 15:29, 5 May 2024 (UTC)

In a sense yes, since a n-illion is 10³ⁿ⁺³. However, this observation is original research and we are right to leave it out of the article. Certes (talk) 15:57, 5 May 2024 (UTC)