View source for Names of large numbers

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Two naming scales for [[large numbers]] have been used in English and other European languages since the early modern era: the [[long and short scale]]s. Most English variants use the short scale today, but the long scale remains dominant in many non-English-speaking areas, including [[continental Europe]] and [[Spanish language|Spanish]]-speaking countries in [[Latin America]]. These naming procedures are based on taking the number ''n'' occurring in 10<sup>3''n''+3</sup> (short scale) or 10<sup>6''n''</sup> (long scale) and concatenating Latin roots for its units, tens, and hundreds place, together with the suffix ''-illion''.

Names of numbers above a trillion are rarely used in practice; such large numbers have practical usage primarily in the scientific domain, where powers of ten are expressed as ''10'' with a numeric superscript. However, these somewhat rare names are considered acceptable for approximate statements. For example, the statement "There are approximately 7.1 octillion atoms in an adult human body" is understood to be in short scale of the table below (and is only accurate if referring to short scale rather than long scale). 

[[Indian English]] do not use millions, but have their own system of large numbers including [[lakh]]s (Anglicised as lacs) and [[crore]]s.<ref name=bellos/> English also has many words, such as "zillion", used informally to mean large but unspecified amounts; see [[indefinite and fictitious numbers]].

== Standard dictionary numbers ==

{| class="wikitable"
|-
! rowspan="2" | x
! rowspan="2" valign="top" | Name<br />(SS/LS, LS)
! rowspan="2" valign="top" | [[long and short scales|SS]]<br />(10<sup>3x+3</sup>)
! rowspan="2" valign="top" | [[long and short scales|LS]]<br />(10<sup>6x</sup>, 10<sup>6x+3</sup>)
! colspan="9" | Authorities
|-
! AHD4<ref name=ahdel/>
! CED<ref name=collins/>
! COD<ref name=cambridge/>
! OED2<ref name=oed_2/>
! OEDweb<ref name=oed_web/>
! RHD2<ref name=random/>
! SOED3<ref name=nsoed/>
! W3<ref name=webster/>
! HM<ref name=rowlett/>
|-
| 1 || [[Million]]
| 10<sup>6</sup> || 10<sup>6</sup>
| ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓
|-
|   || [[Milliard]]
| || 10<sup>9</sup>
| ✓ || ✓ || ✓ || ✓ || ✓ || ✓ ||   ||   || ✓
|-
| 2 || [[Billion]]
| 10<sup>9</sup> || 10<sup>12</sup>
| ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓
|-
| 3 || [[Trillion]]
| 10<sup>12</sup> || 10<sup>18</sup>
| ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓
|-
| 4 || Quadrillion
| 10<sup>15</sup> || 10<sup>24</sup>
| ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓
|-
| 5 || Quintillion
| 10<sup>18</sup> || 10<sup>30</sup>
| ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓
|-
| 6 || Sextillion
| 10<sup>21</sup> || 10<sup>36</sup>
| ✓ || ✓ || &nbsp; || ✓ || ✓ || ✓ || ✓ || ✓ || ✓
|- <!--! AHD4 !! CED !! COD !! Dcom !! OED2 !! OEDnew !! RHD2 !! SOED3 !! W3-->
| 7 || Septillion
| 10<sup>24</sup> || 10<sup>42</sup>
| ✓ || ✓ || &nbsp; || ✓ || ✓ || ✓ || ✓ || ✓ || ✓
|-
| 8 || Octillion
| 10<sup>27</sup> || 10<sup>48</sup>
| ✓ || ✓ || &nbsp; || ✓ || ✓ || ✓ || ✓ || ✓ || ✓
|-
| 9 || Nonillion
| 10<sup>30</sup> || 10<sup>54</sup>
| ✓ || ✓ || &nbsp; || ✓ || ✓ || ✓ || ✓ || ✓ || ✓
|-
| 10 || Decillion
| 10<sup>33</sup> || 10<sup>60</sup>
| ✓ || ✓ || &nbsp; || ✓ || ✓ || ✓ || ✓ || ✓ || ✓
|-
| 11 || Undecillion
| 10<sup>36</sup> || 10<sup>66</sup>
| ✓ || ✓ || &nbsp; || &nbsp; || &nbsp; || ✓ || &nbsp; || ✓ || ✓
|-
| 12 || Duodecillion
| 10<sup>39</sup> || 10<sup>72</sup>
| ✓ || ✓ || ✓ || &nbsp; || &nbsp; || ✓ || &nbsp; || ✓ || ✓
|-
| 13 || Tredecillion
| 10<sup>42</sup> || 10<sup>78</sup>
| ✓ || ✓ || &nbsp; || &nbsp; || &nbsp; || ✓ || &nbsp; || ✓ || ✓
|-
| 14 || Quattuordecillion
| 10<sup>45</sup> || 10<sup>84</sup>
| ✓ || ✓ || &nbsp; || &nbsp; || &nbsp; || ✓ || &nbsp; || ✓ || ✓
|-
| 15 || Quindecillion
| 10<sup>48</sup> || 10<sup>90</sup>
| ✓ || ✓ || &nbsp; || &nbsp; || &nbsp; || ✓ || &nbsp; || ✓ || ✓
|-
| 16 || Sexdecillion
| 10<sup>51</sup> || 10<sup>96</sup>
| ✓ || ✓ || &nbsp; || &nbsp; || &nbsp; || ✓ || &nbsp; || ✓ || ✓
|-
| 17 || Septendecillion
| 10<sup>54</sup> || 10<sup>102</sup>
| ✓ || ✓ || &nbsp; || &nbsp; || &nbsp; || ✓ || &nbsp; || ✓ || ✓
|-
| 18 || Octodecillion
| 10<sup>57</sup> || 10<sup>108</sup>
| ✓ || ✓ || &nbsp; || &nbsp; || &nbsp; || ✓ || &nbsp; || ✓ || ✓
|-
| 19 || Novemdecillion
| 10<sup>60</sup> || 10<sup>114</sup>
| ✓ || ✓ || &nbsp; || &nbsp; || &nbsp; || ✓ || &nbsp; || ✓ || ✓
|-
| 20 || Vigintillion
| 10<sup>63</sup> || 10<sup>120</sup>
| ✓ || ✓ || &nbsp; || ✓ || ✓ || ✓ || ✓ || ✓ || ✓
|-
| 100 || Centillion
| 10<sup>303</sup> || 10<sup>600</sup>
| ✓ || ✓ || &nbsp; || ✓ || ✓ || ✓ || &nbsp; || &nbsp; || ✓
|}

Usage:
* [[long and short scales|Short scale]]: [[American English|US]], [[Canadian English|English Canada]], modern [[British English|British]], [[Australian English|Australia]], and [[Eastern Europe]]
* [[long and short scales|Long scale]]: [[French Canadians|French Canada]], older [[British English|British]], [[Western Europe|Western]] & [[Central Europe]]

Apart from ''million'', the words in this list ending with -''illion'' are all derived by adding prefixes (''bi''-, ''tri''-, etc., derived from Latin) to the stem -''illion''.<ref name=farrar/> ''Centillion''<ref name=centillion/> 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'', ''duo{{shy}}quinqua{{shy}}gint{{shy}}illion'', etc.).

{| class="wikitable"
|-
! rowspan="2" valign="top" | Name
! rowspan="2" valign="top" | Value
! colspan="9" | Authorities
|-
! AHD4<ref name=ahdel/>
! CED<ref name=collins/>
! COD<ref name=cambridge/>
! OED2<ref name=oed_2/>
! OEDweb<ref name=oed_web/>
! RHD2<ref name=random/>
! SOED3<ref name=nsoed/>
! W3<ref name=webster/>
! HM<ref name=rowlett/>
|-
| [[Googol]]
| style="text-align:center"| 10<sup>100</sup>
| ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓
|-
| [[Googolplex]] || 10<sup>googol</sup> (10<sup>10<sup>100</sup></sup>)
| ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓ || ✓
|}

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

== Usage of names of large numbers ==

Some names of large numbers, such as ''million'', ''billion'', and ''trillion'', have real referents in human experience, and are encountered in many contexts. At times, the names of large numbers have been forced into common usage as a result of [[hyperinflation]]. The highest numerical value banknote ever printed was a note for 1 sextillion [[pengő]] (10<sup>21</sup> or 1 milliard bilpengő as printed) printed in [[Hungary]] in 1946. In 2009, [[Zimbabwe]] printed a 100&nbsp;trillion (10<sup>14</sup>) [[Zimbabwean dollar]] note, which at the time of printing was worth about US$30.<ref name=zimbabwe/>

Names of larger numbers, however, have a tenuous, artificial existence, rarely found outside definitions, lists, and discussions of how large numbers are named. Even well-established names like ''sextillion'' are rarely used, since in the context of science, including astronomy, where such large numbers often occur, they are nearly always written using [[scientific notation]]. In this notation, powers of ten are expressed as ''10'' with a numeric superscript, e.g. "The X-ray emission of the radio galaxy is {{val|1.3|e=45|u=joules}}." When a number such as 10<sup>45</sup> needs to be referred to in words, it is simply read out as "ten to the forty-fifth" or "ten to the forty-five". This is easier to say and less ambiguous than "quattuordecillion", which means something different in the long scale and the short scale.

When a number represents a quantity rather than a count, [[SI prefix]]es can be used—thus "[[femtosecond]]", not "one quadrillionth of a second"—although often powers of ten are used instead of some of the very high and very low prefixes. In some cases, specialized units are used, such as the astronomer's [[parsec]] and [[light year]] or the particle physicist's [[barn (unit)|barn]].

Nevertheless, large numbers have an intellectual fascination and are of mathematical interest, and giving them names is one way people try to conceptualize and understand them.

One of the earliest examples of this is ''[[The Sand Reckoner]]'', in which [[Archimedes]] gave a system for naming large numbers. To do this, he called the numbers up to a [[myriad]] myriad (10<sup>8</sup>) "first numbers" and called 10<sup>8</sup> itself the "unit of the second numbers". Multiples of this unit then became the second numbers, up to this unit taken a myriad myriad times, 10<sup>8</sup>·10<sup>8</sup>=10<sup>16</sup>. This became the "unit of the third numbers", whose multiples were the third numbers, and so on. Archimedes continued naming numbers in this way up to a myriad myriad times the unit of the 10<sup>8</sup>-th numbers, i.e. <math>(10^8)^{(10^8)}=10^{8\cdot 10^8},</math> and embedded this construction within another copy of itself to produce names for numbers up to <math>((10^8)^{(10^8)})^{(10^8)}=10^{8\cdot 10^{16}}.</math> Archimedes then estimated the number of grains of sand that would be required to fill the known universe, and found that it was no more than "one thousand myriad of the eighth numbers" (10<sup>63</sup>).

Since then, many others have engaged in the pursuit of conceptualizing and naming numbers that have no existence outside 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.{{fact|date=September 2022}}

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.{{fact|date=September 2022}}

== Origins of the "standard dictionary numbers" ==

[[File:Chuquet.gif|right|500px]]

The&nbsp;words ''bymillion'' and ''trimillion'' were first recorded in 1475 in a manuscript of [[Jehan Adam]]. Subsequently, [[Nicolas Chuquet]] wrote a book ''Triparty en la science des nombres'' which was not published during Chuquet's lifetime. However, most of it was copied by [[Estienne de La Roche]] for a portion of his 1520 book, ''[[L'arismetique]]''. Chuquet's book contains a passage in which he shows a large number marked off into groups of six digits, with the comment:

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

<blockquote>
(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).
</blockquote>

Adam and Chuquet used the [[long and short scale|long scale]] of powers of a million; that is, Adam's ''bymillion'' (Chuquet's ''byllion'') denoted 10<sup>12</sup>, and Adam's ''trimillion'' (Chuquet's ''tryllion'') denoted 10<sup>18</sup>.

== The googol family ==

The names ''[[googol]]'' and ''[[googolplex]]'' were invented by [[Edward Kasner]]'s nephew Milton Sirotta and introduced in Kasner and Newman's 1940 book ''[[Mathematics and the Imagination]]''<ref name=kasner/> in the following passage:

{{quote|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 one 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 happen if one tried to write a googolplex, but different people get tired at different times and it would never do to have [[Primo Carnera|Carnera]] a better mathematician than [[Albert Einstein|Dr. Einstein]], simply because he had more endurance. The googolplex is, then, a specific finite number, equal to 1 with a googol zeros after it.}}

{| class="wikitable"
! width=200 | Value
! Name
! Authority
|-
| 10<sup>100</sup> || [[Googol]] || Kasner and Newman, dictionaries (see above)
|-
| 10<sup>googol</sup> = 10{{sup|10{{sup|100}}}} || [[Googolplex]] || Kasner and Newman, dictionaries (see above)
|}

[[John Horton Conway]] and [[Richard K. Guy]]<ref name=conway/> <!-- According to Amazon it was published in 1998--> have suggested that ''N-plex'' be used as a name for 10<sup>N</sup>. This gives rise to the name ''googolplexplex'' for 10<sup>googolplex</sup> = 10{{sup|10{{sup|10{{sup|100}}}}}}. Conway and Guy<ref name=conway/> have proposed that ''N-minex'' be used as a name for 10<sup>−N</sup>, giving rise to the name ''googolminex'' for the [[Reciprocal (mathematics)|reciprocal]] of a googolplex, which is written as 10{{sup|-(10{{sup|100}})}}. None of these names are in wide use.

The names ''googol'' and ''googolplex'' inspired the name of the [[Dot-com company|Internet company]] [[Google]] and its [[corporate headquarters]], the [[Googleplex]], respectively.{{cn|date=December 2023}}

== Extensions of the standard dictionary numbers ==
{{Further|billion|long and short scales}}

This section illustrates several systems for naming large numbers, and shows how they can be extended past ''vigintillion''.

Traditional British usage assigned new names for each power of one million (the [[long and short scale|long scale]]): {{nowrap|1,000,000 {{=}} 1 million}}; {{nowrap|1,000,000<sup>2</sup> {{=}} 1 billion}}; {{nowrap|1,000,000<sup>3</sup> {{=}} 1 trillion}}; and so on. It was adapted from French usage, and is similar to the system that was documented or invented by [[Nicolas Chuquet|Chuquet]].

Traditional American usage (which was also adapted from French usage but at a later date), Canadian, and modern British usage assign new names for each power of one thousand (the [[long and short scale|short scale]]). Thus, a ''billion'' is 1000 × 1000<sup>2</sup> = 10<sup>9</sup>; a ''trillion'' is 1000 × 1000<sup>3</sup> = 10<sup>12</sup>; 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 originally popularized the short scale worldwide, reverted to the long scale.

{{anchor|Petelier long scale}}
The term ''milliard'' is unambiguous and always means 10<sup>9</sup>. It is seldom seen in American usage and rarely in British usage, but frequently in continental European usage. The term is sometimes attributed to French mathematician [[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.

Concerning names ending in -illiard for numbers 10<sup>6''n''+3</sup>, ''milliard'' is certainly in widespread use in languages other than English, but the degree of actual use of the larger terms is questionable. The terms "milliardo" in Italian, "Milliarde" in German, "miljard" in Dutch, "milyar" in Turkish, and "миллиард," milliard (transliterated) in Russian, are standard usage when discussing financial topics.

The naming procedure for large numbers is based on taking the number ''n'' occurring in 10<sup>3''n''+3</sup> (short scale) or 10<sup>6''n''</sup> (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<sup>3·999+3</sup>&nbsp;=&nbsp;10<sup>3000</sup> (short scale) or 10<sup>6·999</sup>&nbsp;=&nbsp;10<sup>5994</sup> (long scale) may be named. The choice of roots and the concatenation procedure is that of the standard dictionary numbers if ''n'' is 9 or smaller. For larger ''n'' (between 10 and 999), prefixes can be constructed based on a system described by Conway and Guy.<ref name=conway/> Today, sexdecillion and novemdecillion are standard dictionary numbers and, using the same reasoning as Conway and Guy did for the numbers up to nonillion, could probably be used to form acceptable prefixes. The Conway–Guy system for forming prefixes:

{| class="wikitable"
|
! Units
! Tens
! Hundreds
|-
! 1
| Un
| <sup>N</sup> Deci
| <sup>NX</sup> Centi
|-
! 2
| Duo
| <sup>MS</sup> Viginti
| <sup>N</sup> Ducenti
|-
! 3
| Tre {{ref|increase|(*)}}
| <sup>NS</sup> Triginta
| <sup>NS</sup> Trecenti
|-
! 4
| Quattuor
| <sup>NS</sup> Quadraginta
| <sup>NS</sup> Quadringenti
|-
! 5
| Quin
| <sup>NS</sup> Quinquaginta
| <sup>NS</sup> Quingenti
|-
! 6
| Se {{ref|increase|(*)}}
| <sup>N</sup> Sexaginta
| <sup>N</sup> Sescenti
|-
! 7
| Septe {{ref|increase|(*)}}
| <sup>N</sup> Septuaginta
| <sup>N</sup> Septingenti
|-
! 8
| Octo
| <sup>MX</sup> Octoginta
| <sup>MX</sup> Octingenti
|-
! 9
| Nove {{ref|increase|(*)}}
| Nonaginta
| Nongenti
|}

:<sup>(*)</sup> {{note|increase}} When preceding a component marked <sup>S</sup> or <sup>X</sup>, "tre" changes to "tres" and "se" to "ses" or "sex"; similarly, when preceding a component marked <sup>M</sup> or <sup>N</sup>, "septe" and "nove" change to "septem" and "novem" or "septen" and "noven".

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<sup>6,000,258</sup>, Conway and Guy co-devised with Allan Wechsler the following set of consistent conventions that permit, in principle, the extension of this system indefinitely to provide English short-scale names for any integer whatsoever.<ref name=conway/> The name of a number 10<sup>3''n''+3</sup>, where ''n'' is greater than or equal to 1000, is formed by concatenating the names of the numbers of the form 10<sup>3''m''+3</sup>, where ''m'' represents each group of comma-separated digits of ''n'', with each but the last "-illion" trimmed to "-illi-", or, in the case of ''m'' = 0, either "-nilli-" or "-nillion".<ref name=conway/> For example, 10<sup>3,000,012</sup>, the 1,000,003rd "-illion" number, equals one "millinillitrillion"; 10<sup>33,002,010,111</sup>, the 11,000,670,036th "-illion" number, equals one "undecillinilli{{shy}}septua{{shy}}ginta{{shy}}ses{{shy}}centilli{{shy}}sestrigint{{shy}}illion"; and 10<sup>29,629,629,633</sup>, the 9,876,543,210th "-illion" number, equals one "nonillise{{shy}}septua{{shy}}ginta{{shy}}octingentillitres{{shy}}quadra{{shy}}ginta{{shy}}quingentillideciducent{{shy}}illion".<ref name=conway/>

The following table shows number names generated by the system described by Conway and Guy for the short and long scales.<ref>{{Cite web|author=Fish|url=https://kyodaisuu.github.io/illion/conway.html|title=Conway's illion converter
|accessdate=March 1, 2023}}</ref>

{| class="wikitable"
! Base -illion<br />([[long and short scale|short scale]])
! Base -illion<br />([[long and short scale|long scale]])
! Value
! US, Canada and modern British<br />([[long and short scale|short scale]])
! Traditional British<br />([[long and short scale|long scale]])
! Traditional European (Peletier long scale)
! SI<br />Symbol
! SI<br />Prefix
|-
| 1
| 1
| 10<sup>6</sup>
| Million
| Million
| Million
| M
| [[Mega-]]
|-
| 2
| 1
| 10<sup>9</sup>
| Billion
| Thousand million
| Milliard
| G
| [[Giga-]]
|-
| 3
| 2
| 10<sup>12</sup>
| Trillion
| Billion
| Billion
| T
| [[Tera-]]
|-
| 4
| 2
| 10<sup>15</sup>
| Quadrillion
| Thousand billion
| Billiard
| P
| [[Peta-]]
|-
| 5
| 3
| 10<sup>18</sup>
| Quintillion
| Trillion
| Trillion
| E
| [[Exa-]]
|-
| 6
| 3
| 10<sup>21</sup>
| Sextillion
| Thousand trillion
| Trilliard
| Z
| [[Zetta-]]
|-
| 7
| 4
| 10<sup>24</sup>
| Septillion
| Quadrillion
| Quadrillion
| Y
| [[Yotta-]]
|-
| 8
| 4
| 10<sup>27</sup>
| Octillion
| Thousand quadrillion
| Quadrilliard
|R
|[[Ronna-]]
|-
| 9
| 5
| 10<sup>30</sup>
| Nonillion
| Quintillion
| Quintillion
|Q
|[[Quetta-]]
|-
| 10
| 5
| 10<sup>33</sup>
| Decillion
| Thousand quintillion
| colspan="3" | Quintilliard
|-
| 11
| 6
| 10<sup>36</sup>
| Undecillion
| Sextillion
| colspan="3" | Sextillion
|-
| 12
| 6
| 10<sup>39</sup>
| Duodecillion
| Thousand sextillion
| colspan="3" | Sextilliard
|-
| 13
| 7
| 10<sup>42</sup>
| Tredecillion
| Septillion
| colspan="3" | Septillion
|-
| 14
| 7
| 10<sup>45</sup>
| Quattuordecillion
| Thousand septillion
| colspan="3" | Septilliard
|-
| 15
| 8
| 10<sup>48</sup>
| Quindecillion
| Octillion
| colspan="3" | Octillion
|-
| 16
| 8
| 10<sup>51</sup>
| Sedecillion
| Thousand octillion
| colspan="3" | Octilliard
|-
| 17
| 9
| 10<sup>54</sup>
| Septendecillion
| Nonillion
| colspan="3" | Nonillion
|-
| 18
| 9
| 10<sup>57</sup>
| Octodecillion
| Thousand nonillion
| colspan="3" | Nonilliard
|-
| 19
| 10
| 10<sup>60</sup>
| Novendecillion
| Decillion
| colspan="3" | Decillion
|-
| 20
| 10
| 10<sup>63</sup>
| Vigintillion
| Thousand decillion
| colspan="3" | Decilliard
|-
| 21
| 11
| 10<sup>66</sup>
| Unvigintillion
| Undecillion
| colspan="3" | Undecillion
|-
| 22
| 11
| 10<sup>69</sup>
| Duovigintillion
| Thousand undecillion
| colspan="3" | Undecilliard
|-
| 23
| 12
| 10<sup>72</sup>
| Tresvigintillion
| Duodecillion
| colspan="3" | Duodecillion
|-
| 24
| 12
| 10<sup>75</sup>
| Quattuor{{shy}}vigint{{shy}}illion
| Thousand duodecillion
| colspan="3" | Duodecilliard
|-
| 25
| 13
| 10<sup>78</sup>
| Quinvigintillion
| Tredecillion
| colspan="3" | Tredecillion
|-
| 26
| 13
| 10<sup>81</sup>
| Sesvigintillion
| Thousand tredecillion
| colspan="3" | Tredecilliard
|-
| 27
| 14
| 10<sup>84</sup>
| Septemvigintillion
| Quattuordecillion
| colspan="3" | Quattuordecillion
|-
| 28
| 14
| 10<sup>87</sup>
| Octovigintillion
| Thousand quattuordecillion
| colspan="3" | Quattuordecilliard
|-
| 29
| 15
| 10<sup>90</sup>
| Novemvigintillion
| Quindecillion
| colspan="3" | Quindecillion
|-
| 30
| 15
| 10<sup>93</sup>
| Trigintillion
| Thousand quindecillion
| colspan="3" | Quindecilliard
|-
| 31
| 16
| 10<sup>96</sup>
| Untrigintillion
| Sedecillion
| colspan="3" | Sedecillion
|-
| 32
| 16
| 10<sup>99</sup>
| Duotrigintillion
| Thousand sedecillion
| colspan="3" | Sedecilliard
|-
| 33
| 17
| 10<sup>102</sup>
| Trestrigintillion
| Septendecillion
| colspan="3" | Septendecillion
|-
| 34
| 17
| 10<sup>105</sup>
| Quattuor{{shy}}trigint{{shy}}illion
| Thousand septendecillion
| colspan="3" | Septendecilliard
|-
| 35
| 18
| 10<sup>108</sup>
| Quintrigintillion
| Octodecillion
| colspan="3" | Octodecillion
|-
| 36
| 18
| 10<sup>111</sup>
| Sestrigintillion
| Thousand octodecillion
| colspan="3" | Octodecilliard
|-
| 37
| 19
| 10<sup>114</sup>
| Septentrigintillion
| Novendecillion
| colspan="3" | Novendecillion
|-
| 38
| 19
| 10<sup>117</sup>
| Octotrigintillion
| Thousand novendecillion
| colspan="3" | Novendecilliard
|-
| 39
| 20
| 10<sup>120</sup>
| Noventrigintillion
| Vigintillion
| colspan="3" | Vigintillion
|-
| 40
| 20
| 10<sup>123</sup>
| Quadragintillion
| Thousand vigintillion
| colspan="3" | Vigintilliard
|-
| 50
| 25
| 10<sup>153</sup>
| Quinquagintillion
| Thousand quinvigintillion
| colspan="3" | Quinvigintilliard
|-
| 60
| 30
| 10<sup>183</sup>
| Sexagintillion
| Thousand trigintillion
| colspan="3" | Trigintilliard
|-
| 70
| 35
| 10<sup>213</sup>
| Septuagintillion
| Thousand quintrigintillion
| colspan="3" | Quintrigintilliard
|-
| 80
| 40
| 10<sup>243</sup>
| Octogintillion
| Thousand quadragintillion
| colspan="3" | Quadragintilliard
|-
| 90
| 45
| 10<sup>273</sup>
| Nonagintillion
| Thousand quin{{shy}}quadra{{shy}}gint{{shy}}illion
| colspan="3" | Quin{{shy}}quadra{{shy}}gint{{shy}}illiard
|-
| 100
| 50
| 10<sup>303</sup>
| Centillion
| Thousand quinquagintillion
| colspan="3" | Quinquagintilliard
|-
| 101
| 51
| 10<sup>306</sup>
| Uncentillion
| Unquinquagintillion
| colspan="3" | Unquinquagintillion
|-
| 110
| 55
| 10<sup>333</sup>
| Decicentillion
| Thousand quin{{shy}}quinqua{{shy}}gint{{shy}}illion
| colspan="3" | Quin{{shy}}quinqua{{shy}}gint{{shy}}illiard
|-
| 111
| 56
| 10<sup>336</sup>
| Undecicentillion
| Ses{{shy}}quinqua{{shy}}gint{{shy}}illion
| colspan="3" | Ses{{shy}}quinqua{{shy}}gint{{shy}}illion
|-
| 120
| 60
| 10<sup>363</sup>
| Viginticentillion
| Thousand sexagintillion
| colspan="3" | Sexagintilliard
|-
| 121
| 61
| 10<sup>366</sup>
| Unviginticentillion
| Unsexagintillion
| colspan="3" | Unsexagintillion
|-
| 130
| 65
| 10<sup>393</sup>
| Trigintacentillion
| Thousand quinsexagintillion
| colspan="3" | Quinsexagintilliard
|-
| 140
| 70
| 10<sup>423</sup>
| Quadra{{shy}}gintacent{{shy}}illion
| Thousand septuagintillion
| colspan="3" | Septuagintilliard
|-
| 150
| 75
| 10<sup>453</sup>
| Quinqua{{shy}}gintacent{{shy}}illion
| Thousand quin{{shy}}septua{{shy}}gint{{shy}}illion
| colspan="3" | Quin{{shy}}septua{{shy}}gint{{shy}}illiard
|-
| 160
| 80
| 10<sup>483</sup>
| Sexagintacentillion
| Thousand octogintillion
| colspan="3" | Octogintilliard
|-
| 170
| 85
| 10<sup>513</sup>
| Septuagintacentillion
| Thousand quinoctogintillion
| colspan="3" | Quinoctogintilliard
|-
| 180
| 90
| 10<sup>543</sup>
| Octogintacentillion
| Thousand nonagintillion
| colspan="3" | Nonagintilliard
|-
| 190
| 95
| 10<sup>573</sup>
| Nonagintacentillion
| Thousand quinnonagintillion
| colspan="3" | Quinnonagintilliard
|-
| 200
| 100
| 10<sup>603</sup>
| Ducentillion
| Thousand centillion
| colspan="3" | Centilliard
|-
| 300
| 150
| 10<sup>903</sup>
| Trecentillion
| Thousand quinqua{{shy}}gintacent{{shy}}illion
| colspan="3" | Quinqua{{shy}}gintacent{{shy}}illiard
|-
| 400
| 200
| 10<sup>1203</sup>
| Quadringentillion
| Thousand ducentillion
| colspan="3" | Ducentilliard
|-
| 500
| 250
| 10<sup>1503</sup>
| Quingentillion
| Thousand quinqua{{shy}}gintaducent{{shy}}illion
| colspan="3" | Quinqua{{shy}}gintaducent{{shy}}illiard
|-
| 600
| 300
| 10<sup>1803</sup>
| Sescentillion
| Thousand trecentillion
| colspan="3" | Trecentilliard
|-
| 700
| 350
| 10<sup>2103</sup>
| Septingentillion
| Thousand quinqua{{shy}}gintatrecent{{shy}}illion
| colspan="3" | Quinqua{{shy}}gintatrecent{{shy}}illiard
|-
| 800
| 400
| 10<sup>2403</sup>
| Octingentillion
| Thousand quadringentillion
| colspan="3" | Quadringentilliard
|-
| 900
| 450
| 10<sup>2703</sup>
| Nongentillion
| Thousand quinqua{{shy}}ginta{{shy}}quadringent{{shy}}illion
| colspan="3" | Quinqua{{shy}}ginta{{shy}}quadringent{{shy}}illiard
|-
| 1000
| 500
| 10<sup>3003</sup>
| Millinillion <ref name=stewart/>
| Thousand quingentillion
| colspan="3" | Quingentilliard
|}

{| class="wikitable" style=max-width:10em
! rowspan=2 style=max-width:1em | Value
! rowspan=2 style=max-width:1em| Name
! colspan="3" style=max-width:8em | Equivalent
|-
! US, Canadian and modern British<br />([[long and short scale|short scale]])
! Traditional British<br />([[long and short scale|long scale]])
! Traditional European (Peletier long scale)
|-
| 10<sup>100</sup>
| [[Googol]]
| Ten duotrigintillion
| Ten thousand sedecillion
| Ten sedecilliard
|-
| 10{{sup|10{{sup|100}}}}
| [[Googolplex]]
| {{ref|googleplex-shortscale-calculation|[1]}} Ten trilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}trestrigintatrecentilli{{shy}}duotrigintatrecentillion
| {{ref|googleplex-longscale-calculation|[2]}} Ten thousand milli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentillion
| {{ref|googleplex-longscale-calculation|[2]}} Ten milli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilli{{shy}}sesexagintasescentilliard
|}
:{{note|googleplex-shortscale-calculation|[1]}} Googolplex's short scale name is derived from it equal to ten of the 3,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}333,{{0ws}}332nd "-illion"s (This is the value of n when 10 × 10{{sup|(3n + 3)}} = 10{{sup|10{{sup|100}}}})
:{{note|googleplex-longscale-calculation|[2]}} Googolplex's long scale name (both traditional British and traditional European) is derived from it being equal to ten thousand of the 1,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666,{{0ws}}666th "-illion"s (This is the value of n when 10,000 × 10{{sup|6n}} = 10{{sup|10{{sup|100}}}}).

== Binary prefixes ==

The [[International System of Quantities]] (ISQ) defines a series of prefixes denoting integer powers of 1024 between 1024<sup>1</sup> and 1024<sup>8</sup>.<ref name=iec_80000/>

{| class="wikitable"
! Power
! Value
! ISQ<br />symbol
! ISQ<br />prefix
|-
| 1
| 1024<sup>1</sup>
| Ki
| [[Kibi-]]
|-
| 2
| 1024<sup>2</sup>
| Mi
| [[Mebi-]]
|-
| 3
| 1024<sup>3</sup>
| Gi
| [[Gibi-]]
|-
| 4
| 1024<sup>4</sup>
| Ti
| [[Tebi-]]
|-
| 5
| 1024<sup>5</sup>
| Pi
| [[Pebi-]]
|-
| 6
| 1024<sup>6</sup>
| Ei
| [[Exbi-]]
|-
| 7
| 1024<sup>7</sup>
| Zi
| [[Zebi-]]
|-
| 8
| 1024<sup>8</sup>
| Yi
| [[Yobi-]]
|}

== Other named large numbers used in mathematics, physics and chemistry ==

{{Div col|colwidth=15em}}
* [[Avogadro number]]
* [[Graham's number]]
* [[Skewes's number]]
* [[Steinhaus–Moser notation]]
* [[TREE(3)]]
* [[Rayo's number]]
* [[SSCG(3)]]
{{Div col end}}

== See also ==

{{Portal|Mathematics}}
{{Div col}}
* {{annotated link|-yllion}}
* {{annotated link|Infinity}}
* {{annotated link|Asaṃkhyeya}}
* {{annotated link|Chinese numerals}}
* {{annotated link|History of large numbers}}
* {{annotated link|Indefinite and fictitious numbers}}
* {{annotated link|Indian numbering system}}
* {{annotated link|Japanese numerals}}
* {{annotated link|Knuth's up-arrow notation}}
* {{annotated link|Law of large numbers}}
* {{annotated link|List of numbers}}
* {{annotated link|Long and short scale}}
* {{annotated link|Metric prefix}}
* {{annotated link|Names of small numbers}}
* {{annotated link|Numeral (linguistics)|Number names}}
* {{annotated link|Number prefix}}
* {{annotated link|Orders of magnitude}}
* {{annotated link|Orders of magnitude (data)}}
* {{annotated link|Orders of magnitude (numbers)}}
* {{annotated link|Power of 10}}
{{div col end}}

== References ==

{{reflist|30em|refs=

<ref name=zimbabwe>
{{cite web
 | title=Zimbabwe rolls out Z$100tr note
 | url=http://news.bbc.co.uk/2/hi/africa/7832601.stm
 | date=2009-01-16
 | publisher=BBC News
 | access-date=2022-09-25
}}
</ref>

<ref name=conway>
{{cite book
 | title=The Book of Numbers
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 | last1=Conway
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}}
</ref>

<ref name=bellos>
{{cite book
 | title=Alex's Adventures in Numberland
 | first1=Alex
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 | year=2011
 | isbn=978-1-4088-0959-4
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}}
</ref>

<ref name=ahdel>
{{cite book
 | title=The American Heritage Dictionary of the English Language
 | year=2000
 | publisher=Houghton Mifflin
 | isbn=0-395-82517-2
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}}
</ref>

<ref name=collins>
{{cite web
 | title=Collins English Dictionary
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}}
</ref>

<ref name=cambridge>
{{cite web
 | title=Cambridge Dictionaries Online
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 | url=http://dictionary.cambridge.org/
}}
</ref>

<ref name=oed_2>
{{cite book
 | title=The Oxford English Dictionary
 | year=1991
 | edition=2nd
 | publisher=Clarendon Press
 | isbn=0-19-861186-2
 | url=https://books.google.com/books?id=dpIwuwEACAAJ
}}
</ref>

<ref name=oed_web>
{{cite web
 | title=Oxford English Dictionary
 | publisher=Oxford University Press
 | url=http://www.oed.com
 | url-access=subscription
}}
</ref>

<ref name=random>
{{cite book
 | title=The Random House Dictionary of the English Language
 | publisher=Random House
 | year=1987
 | edition=2nd
 | isbn=
}}
</ref>

<ref name=nsoed>
{{cite book
 | title=The New Shorter Oxford English Dictionary
 | publisher=Oxford University Press
 | first1=Lesley
 | last1=Brown
 | first2=William
 | last2=Little
 | year=1993
 | isbn=0198612710
 | url=https://books.google.com/books?id=UCzGvQEACAAJ
}}
</ref>

<ref name=webster>
{{cite book
 | title=Webster's Third New International Dictionary of the English Language, Unabridged
 | first1=Noah
 | last1=Webster
 | publisher=Merriam-Webster
 | year=1981
 | isbn=0877792011
 | url=https://books.google.com/books?id=CXR-tTsHo58C
}}
</ref>

<ref name=rowlett>
{{cite web
 | title=How Many? A Dictionary of Units of Measures
 | first1=Russ
 | last1=Rowlett
 | url=http://www.unc.edu/~rowlett/units/index.html
 | archive-url=https://web.archive.org/web/20000301234049/http://www.unc.edu/~rowlett/units/index.html
 | archive-date=2000-03-01
 | publisher=Russ Rowlett and the University of North Carolina at Chapel Hill
 | access-date=2022-09-25
}}
</ref>

<ref name=farrar>
{{cite book
 | title=The History of the English Language
 | first1=Oliver Farrar
 | last1=Emerson
 | publisher=Macmillan and Co.
 | year=1894
 | page=316
 | url=https://books.google.com/books?id=SRM_AAAAYAAJ
}}
</ref>

<ref name=centillion>
{{cite web
 | title=Entry for ''centillion'' in dictionary.com
 | url=http://dictionary.reference.com/search?q=centillion
 | publisher=dictionary.com
 | access-date=2022-09-25
}}
</ref>

<ref name=kasner>
{{cite book
 | title=Mathematics and the Imagination
 | first1=Edward
 | last1=Kasner
 | first2=James
 | last2=Newman
 | publisher=Simon and Schuster
 | year=1940
 | isbn=0-486-41703-4
 | url=https://books.google.com/books?id=-bXDAgAAQBAJ
}}
</ref>

<!-- <ref name=bowers>
{{cite book
 | title=Infinity Scrapers
 | first1=Jonathan
 | last1=Bowers
 | publisher=Polytope
 | year=2010
}}
</ref> -->

<ref name=stewart>
{{cite book
 | title=Infinity: A Very Short Introduction
 | first1=Ian
 | last1=Stewart
 | publisher=Oxford University Press
 | year=2017
 | isbn=978-0-19-875523-4
 | page=20
 | url=https://books.google.com/books?id=iewwDgAAQBAJ
}}
</ref>

<ref name=iec_80000>
{{cite web
 | title=IEC 80000-13:2008
 | date=15 April 2008
 | url=https://www.iso.org/standard/31898.html
 | publisher=[[International Organization for Standardization]]
 | access-date=2022-09-25
}}
</ref>

}}

{{Large numbers}}

{{Use dmy dates|date=July 2017}}
{{DEFAULTSORT:Names Of Large Numbers}}
[[Category:Large numbers|*]]
[[Category:Numeral systems]]
[[Category:Numerals]]
[[Category:Numbers]]
[[Category:Integers]]