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| {{Globalize/West|date=August 2012}}
| | Jerrie Swoboda is what the public can call me and I totally dig who seem to name. Managing people is my day job now. As a girl what Love it if more like is to take up croquet but I can not make it my line of work really. My husband's comments and I chose to maintain in Massachusetts. Go to my website to find out more: http://circuspartypanama.com<br><br>My weblog - [http://circuspartypanama.com clash of clans hack tool download] |
| This article lists and discusses the usage and derivation of '''names of large numbers''', together with their possible extensions.
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| The following table lists those names of [[large number]]s which are found in many English dictionaries and thus have a special claim to being "real words". The "Traditional British" values shown are unused in American English and are becoming rare in British English, but their other language variants are dominant in many non-English-speaking areas, including [[continental Europe]] and [[Spanish language|Spanish]]-speaking countries in [[Latin America]]; see [[Long and short scales]].
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| English also has many words, such as "zillion", used informally to mean large but unspecified amounts; see [[indefinite and fictitious numbers]].
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| ==Standard dictionary numbers==
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| {|class="wikitable"
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| !rowspan="2" valign="top" bgcolor="#039"| Name
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| !rowspan="2" valign="top" bgcolor="#039"| [[long and short scales|Short scale]]<br />(U.S., Canada and<br />modern British)
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| !rowspan="2" valign="top" bgcolor="#039"| [[long and short scales|Long scale]]<br />(continental Europe,<br /> older British)
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| !colspan="9" bgcolor="#039"| Authorities
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| |-bgcolor="#039"
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| ! AHD4<ref>''[[American Heritage Dictionary]]'', 4th edition, ISBN 0-395-82517-2. [http://www.bartleby.com/61]</ref>
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| ! CED<ref>[http://www.collinsdictionary.com/ Collins English Dictionary], 11th Edition, HarperCollins Publishers.</ref>
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| ! COD<ref>[http://dictionary.cambridge.org/ Cambridge Dictionaries Online], Cambridge, UK: Cambridge University Press.</ref>
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| ! OED2<ref>''[[Oxford English Dictionary]]'', 2nd edition, Oxford, UK: Oxford University Press. ISBN 0-19-861186-2 (and addendums since publication in 1989.)</ref>
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| ! OEDnew<ref>''Oxford English Dictionary'', New Edition, Oxford, UK: Oxford University Press. [http://www.oed.com] (subscription required), checked April 2007</ref>
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| ! RHD2<ref>''The [[Random House Dictionary]]'', 2nd Unabridged Edition, 1987, Random House.</ref>
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| ! SOED3<ref>''Shorter Oxford English Dictionary'', 3rd edition, 1993, Oxford: Clarendon Press.</ref>
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| ! W3<ref>''[[Webster's Third New International Dictionary]], Unabridged'', 1993, Merriam-Webster.</ref>
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| ! UM<ref>{{cite web|title=''How Many? A Dictionary of Units of Measures''|publisher=Russ Rowlett and the University of North Carolina at Chapel Hill|url=http://www.unc.edu/~rowlett/units/index.html|accessdate=2009-08-15}}</ref>
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| | [[Million]]
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| |style="text-align:center"| 10<sup>6</sup> ||style="text-align:center"| 10<sup>6</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}}
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| | [[1,000,000,000|Milliard]] || ||style="text-align:center"| 10<sup>9</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || || || {{unicode|✓}}
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| | [[Billion (disambiguation)|Billion]]
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| |style="text-align:center"| 10<sup>9</sup> ||style="text-align:center"| 10<sup>12</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}}
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| | [[Trillion (disambiguation)|Trillion]]
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| |style="text-align:center"| 10<sup>12</sup> ||style="text-align:center"| 10<sup>18</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}}
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| | [[Quadrillion (disambiguation)|Quadrillion]]
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| |style="text-align:center"| 10<sup>15</sup> ||style="text-align:center"| 10<sup>24</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}}
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| | Quintillion
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| |style="text-align:center"| 10<sup>18</sup> ||style="text-align:center"| 10<sup>30</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}}
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| | Sextillion
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| |style="text-align:center"| 10<sup>21</sup> ||style="text-align:center"| 10<sup>36</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}}
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| |- <!--! AHD4 !! CED !! COD !! Dcom !! OED2 !! OEDnew !! RHD2 !! SOED3 !! W3-->
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| | Septillion
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| |style="text-align:center"| 10<sup>24</sup> ||style="text-align:center"| 10<sup>42</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}}
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| | Octillion
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| |style="text-align:center"| 10<sup>27</sup> ||style="text-align:center"| 10<sup>48</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}}
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| | Nonillion
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| |style="text-align:center"| 10<sup>30</sup> ||style="text-align:center"| 10<sup>54</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}}
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| | Decillion
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| |style="text-align:center"| 10<sup>33</sup> ||style="text-align:center"| 10<sup>60</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}}
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| | Undecillion
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| |style="text-align:center"| 10<sup>36</sup> ||style="text-align:center"| 10<sup>66</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || || || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}}
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| | Duodecillion
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| |style="text-align:center"| 10<sup>39</sup> ||style="text-align:center"| 10<sup>72</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || || || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}}
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| | Tredecillion
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| |style="text-align:center"| 10<sup>42</sup> ||style="text-align:center"| 10<sup>78</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || || || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}}
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| | Quattuordecillion
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| |style="text-align:center"| 10<sup>45</sup> ||style="text-align:center"| 10<sup>84</sup>
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| |{{unicode|✓}} || || || || || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}}
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| | Quindecillion (Quinquadecillion)
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| |style="text-align:center"| 10<sup>48</sup> ||style="text-align:center"| 10<sup>90</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || || || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}}
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| | Sexdecillion (Sedecillion)
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| |style="text-align:center"| 10<sup>51</sup> ||style="text-align:center"| 10<sup>96</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || || || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}}
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| | Septendecillion
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| |style="text-align:center"| 10<sup>54</sup> ||style="text-align:center"| 10<sup>102</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || || || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}}
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| | Octodecillion
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| |style="text-align:center"| 10<sup>57</sup> ||style="text-align:center"| 10<sup>108</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || || || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}}
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| | Novemdecillion (Novendecillion)
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| |style="text-align:center"| 10<sup>60</sup> ||style="text-align:center"| 10<sup>114</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || || || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}}
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| | Vigintillion
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| |style="text-align:center"| 10<sup>63</sup> ||style="text-align:center"| 10<sup>120</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}}
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| | [[Centillion]]
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| |style="text-align:center"| 10<sup>303</sup> ||style="text-align:center"| 10<sup>600</sup>
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| |{{unicode|✓}} || {{unicode|✓}} || || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || || || {{unicode|✓}}
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| |}
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| {|class="wikitable"
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| !rowspan="2" valign="top" bgcolor=#039"| Name
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| !rowspan="2" valign="top" bgcolor=#039"| Value
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| !colspan="9" bgcolor="#039"| Authorities
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| |-bgcolor="#039"
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| ! AHD4 !! CED !! COD !! OED2 !! OEDnew !! RHD2 !! SOED3 !! W3 !! UM
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| | [[Googol]]
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| |style="text-align:center"| 10<sup>100</sup>
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| | [[Googolplex]] || 10<sup>[[Googol]]</sup>
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| | {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}} || {{unicode|✓}}
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| |}
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| 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>p. 316, ''The History of the English Language'', [[Oliver Farrar Emerson]], New York, London: Macmillan and Co., 1894.</ref> ''Centillion''<ref>[http://dictionary.reference.com/search?q=centillion Entry for ''centillion'' in the ''American Heritage Dictionary'']</ref> 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.).
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| All of the dictionaries included ''googol'' and ''googolplex'', generally crediting it to the Kasner and Newman book and to Kasner's nephew. 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".
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| ==Usage of names of large numbers==
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| 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 trillion (10<sup>14</sup>) [[Zimbabwean dollar]] note, which at the time of printing was only worth about US$30.<ref name=zimbabwe>{{cite web|url=http://news.bbc.co.uk/2/hi/africa/7832601.stm|title=Zimbabwe rolls out Z$100tr note|publisher=BBC News|date=January 16, 2009|accessdate=2009-01-16}}</ref>
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| Names of larger numbers, however, have a tenuous, artificial existence, rarely found outside definitions, lists, and discussions of the ways in which large numbers are named. Even well-established names like ''sextillion'' are rarely used, since in the contexts of science, astronomy, and engineering, 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=ergs}}." When a number such as 10<sup>45</sup> 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 in the long scale and the short scale.
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| 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]].
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| Nevertheless, large numbers have an intellectual fascination and are of mathematical interest, and giving them names is one of the ways in which people try to conceptualize and understand them.
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| One of the first 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>\left((10^8)^{(10^8)}\right)^{(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>).
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| 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.
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| 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.
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| ==Origins of the "standard dictionary numbers"==
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| [[File:Chuquet.gif|right|500px]]
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| The 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:
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| <blockquote>
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| 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
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| </blockquote>
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| <blockquote>
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| (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).
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| </blockquote>
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| Chuquet is sometimes credited with inventing the names ''million'', ''billion'', ''trillion'', ''quadrillion'', and so forth. This is an oversimplification.
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| ''Million'' was certainly not invented by Adam or Chuquet. ''Milion'' is an Old French word thought to derive from Italian ''milione'', an intensification of ''mille'', a thousand. That is, a ''million'' is a ''big thousand''.
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| 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, extended the naming scheme and invented the names for the higher powers.
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| Chuquet's names are only similar to, not identical to, the modern ones.
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| Adam and Chuquet used the [[long and short scales|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>.
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| ==An ''aide-memoire''==
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| {{unreferencedsection|date=December 2013}}
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| It can be a problem to find the values for large numbers, either in scientific notation or in sheer digits. Every number listed in this article larger than a million has two values: one in the short scale, where successive names differ by a factor of one thousand, and another in the long scale, where successive names differ by a factor of one million.
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| An easy way to find the value of the above numbers in the short scale (as well as the number of zeroes needed to write them) is to take the number indicated by the prefix (such as 2 in ''bi''llion, 4 in ''quadri''llion, 18 in ''octodec''illion, etc.), add one to it, and multiply that result by 3. For example, in a trillion, the prefix is ''tri'', meaning 3. Adding 1 to it gives 4. Now multiplying 4 by 3 gives us 12, which is the power to which 10 is to be raised to express a short-scale trillion in scientific notation: one trillion = 10<sup>12</sup>.
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| In the long scale, this is done simply by multiplying the number from the prefix by 6. For example, in a billion, the prefix is ''bi'', meaning 2. Multiplying 2 by 6 gives us 12, which is the power to which 10 is to be raised to express a long-scale billion in scientific notation: one billion = 10<sup>12</sup>. The intermediate values (billiard, trilliard, etc.) can be converted in a similar fashion, by adding ½ to the number from the prefix and then multiplying by six. For example, in a septilliard, the prefix is ''sept'', meaning 7. Multiplying 7½ by 6 yields 45, and one septilliard equals 10<sup>45</sup>. Doubling the prefix and adding one then multiplying the result by three would give the same result.
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| These mechanisms are illustrated in the table in the article on [[long and short scales]].
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| Note that when writing out large numbers using this system, one should place a comma or space after every three digits, starting from the right and moving left.
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| ==The googol family==
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| The names ''googol'' and ''googolplex'' were invented by [[Edward Kasner]]'s nephew, [[Milton Sirotta]], and introduced in Kasner and Newman's 1940 book,
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| ''[[Mathematics and the Imagination]]'',<ref>Kasner, Edward and James Newman, ''Mathematics and the Imagination,'' 1940, Simon and Schuster, New York.</ref>
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| in the following passage:
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| <blockquote>
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| 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 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 [[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.
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| </blockquote>
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| {|class="wikitable"
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| ! width=200 | Value
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| ! Name
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| ! Authority
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| | 10<sup>100</sup> || [[Googol]] || Kasner and Newman, dictionaries (see above)
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| | 10<sup>googol</sup> = <math>\,\!10^{10^{100}}</math> || [[Googolplex]] || Kasner and Newman, dictionaries (see above)
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| |}
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| Conway and Guy<ref name=a>''The Book of Numbers'', J. H. Conway and R. K. Guy, New York: Springer-Verlag, 1996, pp. 15–16. ISBN 0-387-97993-X.</ref> <!-- According to Amazon it was published in 1998-->
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| 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>. This number (ten to the power of a googolplex) is also known as a googolduplex and googolplexian.<ref>Bowers, Jonathan. "Infinity Scrapers". Polytope, 2010.</ref> Conway and Guy<ref name=a /> 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. None of these names are in wide use, nor are any currently found in dictionaries.
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| ==Extensions of the standard dictionary numbers==
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| {{refimprove section|date=June 2006}}
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| This table illustrates several systems for naming large numbers, and shows how they can be extended past ''vigintillion''.
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| Traditional British usage assigned new names for each power of one million (the [[long and short scales|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]].
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| Traditional American usage (which, oddly enough, was also adapted from French usage but at a later date), Canadian and modern British usage, assigns new names for each power of one thousand (the [[long and short scales|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.
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| Traditional French usage has varied; in 1948, France, which had been using the short scale, reverted to the long scale.
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| The term ''milliard'' is unambiguous and always means 10<sup>9</sup>. 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.
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| With regard to names ending in -illiard for numbers 10<sup>6n+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 "Milliarde" in German, "miljard" in Dutch, "milyar" in Turkish and "миллиард" in Russian are standard usage when discussing financial topics.
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| The naming procedure for large numbers is based on taking the number ''n'' occurring in 10<sup>3n+3</sup> (short scale) or 10<sup>6n</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> = 10<sup>3000</sup> (short scale) or 10<sup>6·999</sup> = 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 20 or smaller, and, for larger ''n'' (between 21 and 999), is due to [[John Horton Conway]] and [[Richard Guy]]:<ref name=a />
| |
| | |
| {| 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
| |
| |Quinqua
| |
| |<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” increases to “tres” and “se” to “ses” or “sex”; similarly, when preceding a component marked <sup>M</sup> or <sup>N</sup>, “septe” and “nove” increase 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 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.<ref name=a />
| |
| | |
| '''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)|billion]] and [[long and short scales]].
| |
| | |
| {| class="wikitable"
| |
| !Base -illion<br />([[long and short scales|short scale]])
| |
| !Value
| |
| ! U.S., Canada and modern British<br />([[long and short scales|short scale]])
| |
| !Traditional British<br />([[long and short scales|long scale]])
| |
| !Traditional European ([[Jacques Peletier du Mans|Peletier]])<br />([[long and short scales|long scale]])
| |
| !SI<br />Symbol
| |
| !SI<br />Prefix
| |
| |-
| |
| | 1
| |
| | 10<sup>6</sup>
| |
| | Million
| |
| | Million
| |
| | Million
| |
| | M
| |
| | [[Mega-]]
| |
| |-
| |
| | 2
| |
| | 10<sup>9</sup>
| |
| | Billion
| |
| | Thousand million
| |
| | Milliard
| |
| | G
| |
| | [[Giga-]]
| |
| |-
| |
| | 3
| |
| | 10<sup>12</sup>
| |
| | Trillion
| |
| | Billion
| |
| | Billion
| |
| | T
| |
| | [[Tera-]]
| |
| |-
| |
| | 4
| |
| | 10<sup>15</sup>
| |
| | Quadrillion
| |
| | Thousand billion
| |
| | Billiard
| |
| | P
| |
| | [[Peta-]]
| |
| |-
| |
| | 5
| |
| | 10<sup>18</sup>
| |
| | Quintillion
| |
| | Trillion
| |
| | Trillion
| |
| | E
| |
| | [[Exa-]]
| |
| |-
| |
| | 6
| |
| | 10<sup>21</sup>
| |
| | Sextillion
| |
| | Thousand trillion
| |
| | Trilliard
| |
| | Z
| |
| | [[Zetta-]]
| |
| |-
| |
| | 7
| |
| | 10<sup>24</sup>
| |
| | Septillion
| |
| | Quadrillion
| |
| | Quadrillion
| |
| | Y
| |
| | [[Yotta-]]
| |
| |-
| |
| | 8
| |
| | 10<sup>27</sup>
| |
| | Octillion
| |
| | Thousand quadrillion
| |
| | Quadrilliard
| |
| |-
| |
| | 9
| |
| | 10<sup>30</sup>
| |
| | Nonillion
| |
| | Quintillion
| |
| | Quintillion
| |
| |-
| |
| | 10
| |
| | 10<sup>33</sup>
| |
| | Decillion
| |
| | Thousand quintillion
| |
| | Quintilliard
| |
| |-
| |
| | 11
| |
| | 10<sup>36</sup>
| |
| | Undecillion
| |
| | Sextillion
| |
| | Sextillion
| |
| |-
| |
| | 12
| |
| | 10<sup>39</sup>
| |
| | Duodecillion
| |
| | Thousand sextillion
| |
| | Sextilliard
| |
| |-
| |
| | 13
| |
| | 10<sup>42</sup>
| |
| | Tredecillion
| |
| | Septillion
| |
| | Septillion
| |
| |-
| |
| | 14
| |
| | 10<sup>45</sup>
| |
| | Quattuordecillion
| |
| | Thousand septillion
| |
| | Septilliard
| |
| |-
| |
| | 15
| |
| | 10<sup>48</sup>
| |
| | Quinquadecillion
| |
| | Octillion
| |
| | Octillion
| |
| |-
| |
| | 16
| |
| | 10<sup>51</sup>
| |
| | Sedecillion
| |
| | Thousand octillion
| |
| | Octilliard
| |
| |-
| |
| | 17
| |
| | 10<sup>54</sup>
| |
| | Septendecillion
| |
| | Nonillion
| |
| | Nonillion
| |
| |-
| |
| | 18
| |
| | 10<sup>57</sup>
| |
| | Octodecillion
| |
| | Thousand nonillion
| |
| | Nonilliard
| |
| |-
| |
| | 19
| |
| | 10<sup>60</sup>
| |
| | Novendecillion
| |
| | Decillion
| |
| | Decillion
| |
| |-
| |
| | 20
| |
| | 10<sup>63</sup>
| |
| | Vigintillion
| |
| | Thousand decillion
| |
| | Decilliard
| |
| |-
| |
| | 21
| |
| | 10<sup>66</sup>
| |
| | Unvigintillion
| |
| | Undecillion
| |
| | Undecillion
| |
| |-
| |
| | 22
| |
| | 10<sup>69</sup>
| |
| | Duovigintillion
| |
| | Thousand undecillion
| |
| | Undecilliard
| |
| |-
| |
| | 23
| |
| | 10<sup>72</sup>
| |
| | Tresvigintillion
| |
| | Duodecillion
| |
| | Duodecillion
| |
| |-
| |
| | 24
| |
| | 10<sup>75</sup>
| |
| | Quattuorvigintillion
| |
| | Thousand duodecillion
| |
| | Duodecilliard
| |
| |-
| |
| | 25
| |
| | 10<sup>78</sup>
| |
| | Quinquavigintillion
| |
| | Tredecillion
| |
| | Tredecillion
| |
| |-
| |
| | 26
| |
| | 10<sup>81</sup>
| |
| | Sesvigintillion
| |
| | Thousand tredecillion
| |
| | Tredecilliard
| |
| |-
| |
| | 27
| |
| | 10<sup>84</sup>
| |
| | Septemvigintillion
| |
| | Quattuordecillion
| |
| | Quattuordecillion
| |
| |-
| |
| | 28
| |
| | 10<sup>87</sup>
| |
| | Octovigintillion
| |
| | Thousand quattuordecillion
| |
| | Quattuordecilliard
| |
| |-
| |
| | 29
| |
| | 10<sup>90</sup>
| |
| | Novemvigintillion
| |
| | Quindecillion
| |
| | Quindecillion
| |
| |-
| |
| | 30
| |
| | 10<sup>93</sup>
| |
| | Trigintillion
| |
| | Thousand quindecillion
| |
| | Quindecilliard
| |
| |-
| |
| | 31
| |
| | 10<sup>96</sup>
| |
| | Untrigintillion
| |
| | Sedecillion
| |
| | Sedecillion
| |
| |-
| |
| | 32
| |
| | 10<sup>99</sup>
| |
| | Duotrigintillion
| |
| | Thousand sedecillion
| |
| | Sedecilliard
| |
| |-
| |
| | 33
| |
| | 10<sup>102</sup>
| |
| | Trestrigintillion
| |
| | Septendecillion
| |
| | Septendecillion
| |
| |-
| |
| | 34
| |
| | 10<sup>105</sup>
| |
| | Quattuortrigintillion
| |
| | Thousand septendecillion
| |
| | Septendecilliard
| |
| |-
| |
| | 35
| |
| | 10<sup>108</sup>
| |
| | Quinquatrigintillion
| |
| | Octodecillion
| |
| | Octodecillion
| |
| |-
| |
| | 36
| |
| | 10<sup>111</sup>
| |
| | Sestrigintillion
| |
| | Thousand octodecillion
| |
| | Octodecilliard
| |
| |-
| |
| | 37
| |
| | 10<sup>114</sup>
| |
| | Septentrigintillion
| |
| | Novendecillion
| |
| | Novendecillion
| |
| |-
| |
| | 38
| |
| | 10<sup>117</sup>
| |
| | Octotrigintillion
| |
| | Thousand novendecillion
| |
| | Novendecilliard
| |
| |-
| |
| | 39
| |
| | 10<sup>120</sup>
| |
| | Noventrigintillion
| |
| | Vigintillion
| |
| | Vigintillion
| |
| |-
| |
| | 40
| |
| | 10<sup>123</sup>
| |
| | Quadragintillion
| |
| | Thousand vigintillion
| |
| | Vigintilliard
| |
| |-
| |
| | 50
| |
| | 10<sup>153</sup>
| |
| | Quinquagintillion
| |
| | Thousand quinquavigintillion
| |
| | Quinquavigintilliard
| |
| |-
| |
| | 60
| |
| | 10<sup>183</sup>
| |
| | Sexagintillion
| |
| | Thousand trigintillion
| |
| | Trigintilliard
| |
| |-
| |
| | 70
| |
| | 10<sup>213</sup>
| |
| | Septuagintillion
| |
| | Thousand quinquatrigintillion
| |
| | Quinquatrigintilliard
| |
| |-
| |
| | 80
| |
| | 10<sup>243</sup>
| |
| | Octogintillion
| |
| | Thousand quadragintillion
| |
| | Quadragintilliard
| |
| |-
| |
| | 90
| |
| | 10<sup>273</sup>
| |
| | Nonagintillion
| |
| | Thousand quinquaquadragintillion
| |
| | Quinquaquadragintilliard
| |
| |-
| |
| | 100
| |
| | 10<sup>303</sup>
| |
| | Centillion
| |
| | Thousand quinquagintillion
| |
| | Quinquagintilliard
| |
| |-
| |
| | 101
| |
| | 10<sup>306</sup>
| |
| | Uncentillion
| |
| | Unquinquagintillion
| |
| | Unquinquagintillion
| |
| |-
| |
| | 102
| |
| | 10<sup>309</sup>
| |
| | Duocentillion
| |
| | Thousand unquinquagintillion
| |
| | Unquinquagintilliard
| |
| |-
| |
| | 103
| |
| | 10<sup>312</sup>
| |
| | Trescentillion
| |
| | Duoquinquagintillion
| |
| | Duoquinquagintillion
| |
| |-
| |
| | 110
| |
| | 10<sup>333</sup>
| |
| | Decicentillion
| |
| | Thousand quinquaquinquagintillion
| |
| | Quinquaquinquagintilliard
| |
| |-
| |
| | 111
| |
| | 10<sup>336</sup>
| |
| | Undecicentillion
| |
| | Sesquinquagintillion
| |
| | Sesquinquagintillion
| |
| |-
| |
| | 120
| |
| | 10<sup>363</sup>
| |
| | Viginticentillion
| |
| | Thousand sexagintillion
| |
| | Sexagintilliard
| |
| |-
| |
| | 121
| |
| | 10<sup>366</sup>
| |
| | Unviginticentillion
| |
| | Unsexagintillion
| |
| | Unsexagintillion
| |
| |-
| |
| | 130
| |
| | 10<sup>393</sup>
| |
| | Trigintacentillion
| |
| | Thousand quinquasexagintillion
| |
| | Quinquasexagintilliard
| |
| |-
| |
| | 140
| |
| | 10<sup>423</sup>
| |
| | Quadragintacentillion
| |
| | Thousand septuagintillion
| |
| | Septuagintilliard
| |
| |-
| |
| | 150
| |
| | 10<sup>453</sup>
| |
| | Quinquagintacentillion
| |
| | Thousand quinquaseptuagintillion
| |
| | Quinquaseptuagintilliard
| |
| |-
| |
| | 160
| |
| | 10<sup>483</sup>
| |
| | Sexagintacentillion
| |
| | Thousand octogintillion
| |
| | Octogintilliard
| |
| |-
| |
| | 170
| |
| | 10<sup>513</sup>
| |
| | Septuagintacentillion
| |
| | Thousand quinquaoctogintillion
| |
| | Quinquaoctogintilliard
| |
| |-
| |
| | 180
| |
| | 10<sup>543</sup>
| |
| | Octogintacentillion
| |
| | Thousand nonagintillion
| |
| | Nonagintilliard
| |
| |-
| |
| | 190
| |
| | 10<sup>573</sup>
| |
| | Nonagintacentillion
| |
| | Thousand quinquanonagintillion
| |
| | Quinquanonagintilliard
| |
| |-
| |
| | 200
| |
| | 10<sup>603</sup>
| |
| | Ducentillion
| |
| | Thousand centillion
| |
| | Centilliard
| |
| |-
| |
| | 300
| |
| | 10<sup>903</sup>
| |
| | Trecentillion
| |
| | Thousand quinquagintacentillion
| |
| | Quinquagintacentilliard
| |
| |-
| |
| | 400
| |
| | 10<sup>1203</sup>
| |
| | Quadringentillion
| |
| | Thousand ducentillion
| |
| | Ducentilliard
| |
| |-
| |
| | 500
| |
| | 10<sup>1503</sup>
| |
| | Quingentillion
| |
| | Thousand quinquagintaducentillion
| |
| | Quinquagintaducentilliard
| |
| |-
| |
| | 600
| |
| | 10<sup>1803</sup>
| |
| | Sescentillion
| |
| | Thousand trecentillion
| |
| | Trecentilliard
| |
| |-
| |
| | 700
| |
| | 10<sup>2103</sup>
| |
| | Septingentillion
| |
| | Thousand quinquagintatrecentillion
| |
| | Quinquagintatrecentilliard
| |
| |-
| |
| | 800
| |
| | 10<sup>2403</sup>
| |
| | Octingentillion
| |
| | Thousand quadringentillion
| |
| | Quadringentilliard
| |
| |-
| |
| | 900
| |
| | 10<sup>2703</sup>
| |
| | Nongentillion
| |
| | Thousand quinquagintaquadringentillion
| |
| | Quinquagintaquadringentilliard
| |
| |-
| |
| | 1000
| |
| | 10<sup>3003</sup>
| |
| | Millinillion
| |
| | Thousand quingentillion
| |
| | Quingentilliard
| |
| |}
| |
| | |
| {| class="wikitable"
| |
| !Value
| |
| ! U.S., Canada and modern British<br />([[long and short scales|short scale]])
| |
| !Traditional British<br />([[long and short scales|long scale]])
| |
| !Traditional European ([[Jacques Peletier du Mans|Peletier]])<br />([[long and short scales|long scale]])
| |
| |-
| |
| | 10<sup>100</sup>
| |
| | [[Googol]] (Ten duotrigintillion)
| |
| | [[Googol]] (Ten thousand sedecillion)
| |
| | [[Googol]] (Ten sedecilliard)
| |
| |-
| |
| | <math>10^{10^{100}}\,\!</math>
| |
| | [[Googolplex]]
| |
| | [[Googolplex]]
| |
| | [[Googolplex]]
| |
| |}
| |
| | |
| ==Proposals for new naming system==
| |
| {{See also|-yllion}}
| |
| In 2001, Russ Rowlett, Director of the Center for Mathematics and Science Education at the [[University of North Carolina at Chapel Hill]] proposed that, to avoid confusion, the [[Latin]]-based short scale and long scale systems should be replaced by an unambiguous [[Greek language|Greek]]-based system for naming large numbers that would be based on powers of one thousand.<ref>{{cite web
| |
| | last = Rowlett
| |
| | first = Russ
| |
| | authorlink =
| |
| | coauthors =
| |
| | title = Names for large numbers
| |
| | work =
| |
| | publisher = University of North Carolina
| |
| | date = 2001-11-01
| |
| | url = http://www.unc.edu/~rowlett/units/large.html
| |
| | doi =
| |
| | accessdate = 2008-01-31 }}</ref>
| |
| <!-- nested tables. outer table has three columns, one row.
| |
| each of three inner tables has two columns, many rows. -->
| |
| {|
| |
| |
| |
| {| class="wikitable"
| |
| |-
| |
| ! Value !! Name
| |
| |-
| |
| | 10<sup>3</sup> || Thousand
| |
| |-
| |
| | 10<sup>6</sup> || Million
| |
| |-
| |
| | 10<sup>9</sup> || Gillion
| |
| |-
| |
| | 10<sup>12</sup> || Tetrillion
| |
| |-
| |
| | 10<sup>15</sup> || Pentillion
| |
| |-
| |
| | 10<sup>18</sup> || Hexillion
| |
| |-
| |
| | 10<sup>21</sup> || Heptillion
| |
| |-
| |
| | 10<sup>24</sup> || Oktillion
| |
| |-
| |
| | 10<sup>27</sup> || Ennillion
| |
| |-
| |
| | 10<sup>30</sup> || Dekillion
| |
| |-
| |
| |}
| |
| |
| |
| {| class="wikitable"
| |
| |-
| |
| ! Value !! Name
| |
| |-
| |
| | 10<sup>33</sup> || Hendekillion
| |
| |-
| |
| | 10<sup>36</sup> || Dodekillion
| |
| |-
| |
| | 10<sup>39</sup> || Trisdekillion
| |
| |-
| |
| | 10<sup>42</sup> || Tetradekillion
| |
| |-
| |
| | 10<sup>45</sup> || Pentadekillion
| |
| |-
| |
| | 10<sup>48</sup> || Hexadekillion
| |
| |-
| |
| | 10<sup>51</sup> || Heptadekillion
| |
| |-
| |
| | 10<sup>54</sup> || Oktadekillion
| |
| |-
| |
| | 10<sup>57</sup> || Enneadekillion
| |
| |-
| |
| | 10<sup>60</sup> || Icosillion
| |
| |-
| |
| |}
| |
| |
| |
| {| class="wikitable"
| |
| |-
| |
| ! Value !! Name
| |
| |-
| |
| | 10<sup>63</sup> || Icosihenillion
| |
| |-
| |
| | 10<sup>66</sup> || Icosidillion
| |
| |-
| |
| | 10<sup>69</sup> || Icositrillion
| |
| |-
| |
| | 10<sup>72</sup> || Icositetrillion
| |
| |-
| |
| | 10<sup>75</sup> || Icosipentillion
| |
| |-
| |
| | 10<sup>78</sup> || Icosihexillion
| |
| |-
| |
| | 10<sup>81</sup> || Icosiheptillion
| |
| |-
| |
| | 10<sup>84</sup> || Icosioktillion
| |
| |-
| |
| | 10<sup>87</sup> || Icosiennillion
| |
| |-
| |
| | 10<sup>90</sup> || Triacontillion
| |
| |-
| |
| |}
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| |}
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| ==Other large numbers used in mathematics and physics==
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| * [[Avogadro's number]]
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| * [[Graham's number]]
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| * [[Skewes' number]]
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| * [[Steinhaus–Moser notation]]
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| ==See also==
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| {{Col-begin}}
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| {{Col-1-of-3}}
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| * [[Chinese numerals]]
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| * [[Indefinite and fictitious numbers]]
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| * [[Indian Numbering System]]
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| * [[Knuth's up-arrow notation]]
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| * [[Law of large numbers]]
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| * [[List of numbers]]
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| {{Col-2-of-3}}
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| * [[Names of small numbers]]
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| * [[Nicolas Chuquet]]
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| * [[Numeral (linguistics)|Number names]]
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| * [[Number prefix]]
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| * [[Orders of magnitude]]
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| * [[Orders of magnitude (numbers)]]
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| * [[Orders of magnitude (data)]]
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| * [[Powers of 10]]
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| {{Col-end}}
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| {{Portal|Mathematics}}
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| ==References==
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| {{More footnotes|date=May 2011}}
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| {{Reflist}}
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| | |
| ==External links==
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| * [http://www.mrob.com/pub/math/largenum.html Robert Munafo's Large Numbers]
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| * [http://www.isthe.com/chongo/tech/math/number/howhigh.html ''How high can you count?''] by [[Landon Curt Noll]].
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| * [http://home.kpn.nl/vanadovv/BignumbyN.html Full list of large number names] list sorted by 10<sup>n</sup> and by word length
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| * [http://www.mathcats.com/explore/reallybignumbers.html Big numbers] Educational site, which can name any numbers put into it (up to centillion)
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| * [http://www.isthe.com/cgi-bin/number.cgi The English name of a number] An online tool that prints names of numbers of any size
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| {{Large numbers}}
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| {{DEFAULTSORT:Names Of Large Numbers}}
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| [[Category:Large numbers|*]]
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| [[Category:Numeral systems]]
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| [[Category:Numerals]]
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| {{Link GA|pl}}
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| [[vep:Centillion]]
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