Depending on context (e.g., language, culture, region), some large numbers have names that allow for describing large quantities in a textual, not mathematical, form. For very large values, the text is generally shorter than a decimal numeric representation, although longer than scientific notation.
Two naming scales for large numbers have been used in English and other European languages since the early modern era: the long and short scales. 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-speaking countries in the Americas. These naming procedures are 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 .
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, and in the case of hyperinflation. 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).
The Indian numbering system uses the named numbers common between the long and short scales up to ten thousand. For larger values, it includes named numbers at each multiple of 100, including lakh (105) and crore (107).
English also has words, such as zillion, that are used informally to mean large but unspecified amounts.
Standard dictionary numbers
In the following table, "SS" is used for short scale, and "LS" for "long scale". x Name(SS/LS, LS) SS(103x+3) LS(106x, 106x+3) Appearance in different dictionaries AHD4 CED COD MW OED RHD2 SOED3 W3 HM 1 million 106 106 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ milliard 109 ✓ ✓ ✓ ✓ ✓ ✓ ✓ 2 billion 109 1012 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 3 trillion 1012 1018 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 4 quadrillion 1015 1024 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 5 quintillion 1018 1030 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 6 sextillion 1021 1036 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 7 septillion 1024 1042 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 8 octillion 1027 1048 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 9 nonillion 1030 1054 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 10 decillion 1033 1060 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 11 undecillion 1036 1066 ✓ ✓ ✓ ✓ ✓ ✓ 12 duodecillion 1039 1072 ✓ ✓ ✓ ✓ ✓ ✓ ✓ 13 tredecillion 1042 1078 ✓ ✓ ✓ ✓ ✓ ✓ 14 quattuordecillion 1045 1084 ✓ ✓ ✓ ✓ ✓ ✓ 15 quindecillion 1048 1090 ✓ ✓ ✓ ✓ ✓ ✓ 16 sexdecillion 1051 1096 ✓ ✓ ✓ ✓ ✓ ✓ 17 septendecillion 1054 10102 ✓ ✓ ✓ ✓ ✓ ✓ 18 octodecillion 1057 10108 ✓ ✓ ✓ ✓ ✓ ✓ 19 novemdecillion 1060 10114 ✓ ✓ ✓ ✓ ✓ ✓ 20 vigintillion 1063 10120 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 30 trigintillion 1093 10180 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 40 quadragintillion 10123 10240 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 100 centillion 10303 10600 ✓ ✓ ✓ ✓ ✓ ✓
Usage: Short scale: US, English Canada, modern British, Australia, and Eastern Europe Long scale: French Canada, obsolete British, Western & Central Europe
Obsolete terms such as "billiard" and "trilliard" are listed below under "Extensions of the standard dictionary numbers".
Apart from million, the words in this list ending with are all derived by adding prefixes (bi-, tri-, etc., derived from Latin) to the stem . Centillion appears to be the highest name ending in 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.).
Name Value Authorities AHD4 CED COD MW OED RHD2 SOED3 W3 HM googol 10100 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ googolplex 10googol (1010100) ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
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, particularly in finance and economics. 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 (1021 or 1 milliárd bilpengő as printed) printed in Hungary in 1946. In 2009, Zimbabwe printed a 100 trillion (1014) Zimbabwean dollar note, which at the time of printing was worth about US$30. In global economics, the name of a significantly larger number was used in 2024, when the Russian news outlet RBK stated that the sum of legal claims against Google in Russia totalled 2 undecillion (2) rubles, or US$20 decillion (US $2), a value worth more than all financial assets in the world combined. A Kremlin spokesperson, Dmitry Peskov, stated that this value was symbolic.
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 ." When a number such as 1045 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 prefixes 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.
Large numbers have an intellectual fascination and are of mathematical interest, and giving them names is a way 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 (108) "first numbers" and called 108 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, 108·108=1016. 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 108-th numbers, i.e. and embedded this construction within another copy of itself to produce names for numbers up to 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" (1063).
Origins of the "standard dictionary numbers"
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:
Ou qui veult le premier point peult signiffier million Le second point byllion Le tiers point 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).
Adam and Chuquet used the long scale of powers of a million; that is, Adam's bymillion (Chuquet's byllion) denoted 1012, and Adam's trimillion (Chuquet's tryllion) denoted 1018.
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 in the following passage:
Value Name Authority 10100 googol Kasner and Newman, dictionaries (see above) 10googol = 10 googolplex Kasner and Newman, dictionaries (see above)
John Horton Conway and Richard K. Guy have suggested that N-plex be used as a name for 10N. This gives rise to the name googolplexplex for 10googolplex = 10, which is unofficially known as a googolplexian (or googolduplex) by some googologists. Conway and Guy have proposed that N-minex be used as a name for 10−N, giving rise to the name googolminex for the reciprocal of a googolplex, which is written as 10. None of these names are in wide use.
A googologist from Texas coined the terms giggol and giggolplex for tetrational numbers. Giggol is equal to , or 10 tetrated to 100 and Giggolplex is 10 tetrated to giggol or . If they are written in exponentiation, then they would be power towers of 100 and "a power tower of 100 tens" tens, respectively. They were coined by altering the vowel sound of "googol" and a different definition of "-plex": If or , where is any googolocial function, then -plex
The names googol and googolplex inspired the name of the Internet company Google and its corporate headquarters, the Googleplex, respectively.
Extensions of the standard dictionary numbers
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 scale): ; ; ; 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 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 short scale). Thus, a billion is ; a trillion is ; and so forth. Due to its dominance in the financial world (along with 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.
The term milliard is unambiguous and always means 109. 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 (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 106n+3, 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.