Names of large numbers

Depending on context, 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 or 10⁶ⁿ 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. 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.
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 and crore.
English also has words, such as zillion, that are used informally to mean large but unspecified amounts.

Standard dictionary numbers

Usage:

Short scale: US, English Canada, modern British, Australia, and Eastern Europe
Long scale: French Canada, older British, Western & Central Europe

Apart from million, the words in this list ending with ' are all derived by adding prefixes 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.
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. 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 printed in Hungary in 1946. In 2009, Zimbabwe printed a 100 trillion 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 rubles, or US$20 decillion, 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.
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 "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".

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 cinq^e quyllion Le six^e sixlion Le sept.^e septyllion Le huyt^e ottyllion Le neuf^e nonyllion et ainsi des ault'^s se plus oultre on vouloit preceder

.

Adam and Chuquet used the long scale of powers of a million; that is, Adam's bymillion denoted 10¹², and Adam's trimillion 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
10^googol = 10	googolplex	Kasner and Newman, dictionaries

John Horton Conway and Richard K. Guy have suggested that N-plex be used as a name for 10^N. This gives rise to the name googolplexplex for 10^googolplex = 10. 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 term giggol for a tetrational number. Giggol is equal to, or 10 tetrated to 100. If it is written in exponentiation, then it would be a power tower of 100 tens. It was coined by altering the vowel sound of "googol".
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 : ; ; ; 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, Canadian, and modern British usage assign new names for each power of one thousand. Thus, a billion is ; a trillion is ; and so forth. Due to its dominance in the financial world, 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 , 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 in Russian, are standard usage when discussing financial topics.
The naming procedure for large numbers is based on taking the number n occurring in 10³ⁿ⁺³ or 10⁶ⁿ and concatenating Latin roots for its units, tens, and hundreds place, together with the suffix . If the final root is multisyllabic and ends in a vowel, that vowel is removed; for example, centi + illion = centillion, not centiillion. Monosyllabic final roots ending in vowels only occur when the naming system does not apply, for very small numbers, so they do not have defined behavior. The number "0" is skipped, i.e. it produces the empty string - 103 results in the root for units 3 followed by the root for hundreds 1. In this way, numbers up to 10^3·999+3 = 10³⁰⁰⁰ or 10^6·999 = 10⁵⁹⁹⁴ 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, prefixes can be constructed based on a system described by Conway and Guy. 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:

	Units	Tens	Hundreds
0			-
1	Un	Deci	Centi
2	Duo	Viginti	Ducenti
3	Tre	Triginta	Trecenti
4	Quattuor	Quadraginta	Quadringenti
5	Quinqua	Quinquaginta	Quingenti
6	Se	Sexaginta	Sescenti
7	Septe	Septuaginta	Septingenti
8	Octo	Octoginta	Octingenti
9	Nove	Nonaginta	Nongenti

When preceding a component prefixed with ^S or ^X, a component suffixed with ^S - "tre" - suffixes with an s and a component suffixed with ^SX - "se" - suffixes to match the prefix.
When preceding a component prefixed with ^M or ^N, a component suffixed with ^MN - "septe" and "nove" - suffixes to match the prefix.
Conway and Guy originally used "quinqua" but as a result of Miakinen's suggestion "quin" is mostly used.

The Conway–Guy system disagrees with some standard dictionary names, like "quindecillion", "sexdecillion", and "novemdecillion". Oliver Miakinen argued that since "quindecillion" is a widely accepted term, and the Latin for 15 is actually quindecim and not quinquadecim, the prefix "quinqua-" should be replaced with "quin-". This new prefix is more commonly used nowadays.
Since the system of using Latin prefixes will become ambiguous for numbers with exponents of a size which the Romans rarely counted to, like 10^6,000,258, Conway and Guy 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. The name of a number 10³ⁿ⁺³, where n is greater than or equal to 1000, is formed by concatenating the names of the numbers of the form 10^3m+3, where m represents each group of comma-separated digits of n, with each but the last "" trimmed to "", or, in the case of m = 0, either "-nilli-" or "-nillion". For example, 10^3,000,012, the 1,000,003rd "" number, equals one "millinillitrillion"; 10^{33,002,010,111}, the 11,000,670,036th "" number, equals one "undecillinilliseptuagintasescentillisestrigintillion"; and 10^{29,629,629,633}, the 9,876,543,210th "" number, equals one "nonilliseseptuagintaoctingentillitresquadragintaquingentillideciducentillion".
The following table shows number names generated by the system described by Conway and Guy for the short and long scales. Note that since the scale begins at n=10, the short scale begins at 10³³ and the long scale begins at 10⁶⁰; below that, one is supposed to consult the dictionary.

Base	Base	Value	US, Canada, and modern British	Traditional British	Traditional European
1	1	10⁶	million	million	million
2	1	10⁹	billion	thousand million	milliard
3	2	10¹²	trillion	billion	billion
4	2	10¹⁵	quadrillion	thousand billion	billiard
5	3	10¹⁸	quintillion	trillion	trillion
6	3	10²¹	sextillion	thousand trillion	trilliard
7	4	10²⁴	septillion	quadrillion	quadrillion
8	4	10²⁷	octillion	thousand quadrillion	quadrilliard
9	5	10³⁰	nonillion	quintillion	quintillion
10	5	10³³	decillion	thousand quintillion	quintilliard
11	6	10³⁶	undecillion	sextillion	sextillion
12	6	10³⁹	duodecillion	thousand sextillion	sextilliard
13	7	10⁴²	tredecillion	septillion	septillion
14	7	10⁴⁵	quattuordecillion	thousand septillion	septilliard
15	8	10⁴⁸	quindecillion	octillion	octillion
16	8	10⁵¹	sedecillion	thousand octillion	octilliard
17	9	10⁵⁴	septendecillion	nonillion	nonillion
18	9	10⁵⁷	octodecillion	thousand nonillion	nonilliard
19	10	10⁶⁰	novemdecillion	decillion	decillion
20	10	10⁶³	vigintillion	thousand decillion	decilliard
21	11	10⁶⁶	unvigintillion	undecillion	undecillion
22	11	10⁶⁹	duovigintillion	thousand undecillion	undecilliard
23	12	10⁷²	tresvigintillion	duodecillion	duodecillion
24	12	10⁷⁵	quattuorvigintillion	thousand duodecillion	duodecilliard
25	13	10⁷⁸	quinvigintillion	tredecillion	tredecillion
26	13	10⁸¹	sesvigintillion	thousand tredecillion	tredecilliard
27	14	10⁸⁴	septemvigintillion	quattuordecillion	quattuordecillion
28	14	10⁸⁷	octovigintillion	thousand quattuordecillion	quattuordecilliard
29	15	10⁹⁰	novemvigintillion	quindecillion	quindecillion
30	15	10⁹³	trigintillion	thousand quindecillion	quindecilliard
31	16	10⁹⁶	untrigintillion	sedecillion	sedecillion
32	16	10⁹⁹	duotrigintillion	thousand sedecillion	sedecilliard
33	17	10¹⁰²	trestrigintillion	septendecillion	septendecillion
34	17	10¹⁰⁵	quattuortrigintillion	thousand septendecillion	septendecilliard
35	18	10¹⁰⁸	quintrigintillion	octodecillion	octodecillion
36	18	10¹¹¹	sestrigintillion	thousand octodecillion	octodecilliard
37	19	10¹¹⁴	septentrigintillion	novendecillion	novendecillion
38	19	10¹¹⁷	octotrigintillion	thousand novendecillion	novendecilliard
39	20	10¹²⁰	noventrigintillion	vigintillion	vigintillion
40	20	10¹²³	quadragintillion	thousand vigintillion	vigintilliard
50	25	10¹⁵³	quinquagintillion	thousand quinvigintillion	quinvigintilliard
60	30	10¹⁸³	sexagintillion	thousand trigintillion	trigintilliard
70	35	10²¹³	septuagintillion	thousand quintrigintillion	quintrigintilliard
80	40	10²⁴³	octogintillion	thousand quadragintillion	quadragintilliard
90	45	10²⁷³	nonagintillion	thousand quinquadragintillion	quinquadragintilliard
100	50	10³⁰³	centillion	thousand quinquagintillion	quinquagintilliard
101	51	10³⁰⁶	uncentillion	unquinquagintillion	unquinquagintillion
110	55	10³³³	decicentillion	thousand quinquinquagintillion	quinquinquagintilliard
111	56	10³³⁶	undecicentillion	sesquinquagintillion	sesquinquagintillion
120	60	10³⁶³	viginticentillion	thousand sexagintillion	sexagintilliard
121	61	10³⁶⁶	unviginticentillion	unsexagintillion	unsexagintillion
130	65	10³⁹³	trigintacentillion	thousand quinsexagintillion	quinsexagintilliard
140	70	10⁴²³	quadragintacentillion	thousand septuagintillion	septuagintilliard
150	75	10⁴⁵³	quinquagintacentillion	thousand quinseptuagintillion	quinseptuagintilliard
160	80	10⁴⁸³	sexagintacentillion	thousand octogintillion	octogintilliard
170	85	10⁵¹³	septuagintacentillion	thousand quinoctogintillion	quinoctogintilliard
180	90	10⁵⁴³	octogintacentillion	thousand nonagintillion	nonagintilliard
190	95	10⁵⁷³	nonagintacentillion	thousand quinnonagintillion	quinnonagintilliard
200	100	10⁶⁰³	ducentillion	thousand centillion	centilliard
300	150	10⁹⁰³	trecentillion	thousand quinquagintacentillion	quinquagintacentilliard
400	200	10¹²⁰³	quadringentillion	thousand ducentillion	ducentilliard
500	250	10¹⁵⁰³	quingentillion	thousand quinquagintaducentillion	quinquagintaducentilliard
600	300	10¹⁸⁰³	sescentillion	thousand trecentillion	trecentilliard
700	350	10²¹⁰³	septingentillion	thousand quinquagintatrecentillion	quinquagintatrecentilliard
800	400	10²⁴⁰³	octingentillion	thousand quadringentillion	quadringentilliard
900	450	10²⁷⁰³	nongentillion	thousand quinquagintaquadringentillion	quinquagintaquadringentilliard
1000	500	10³⁰⁰³	millinillion	thousand quingentillion	quingentilliard