Names of large numbers

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. 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). 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 (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. <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" (10⁶³).

Origins of the "standard dictionary numbers"

right|500px

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:

<blockquote>

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

</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 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

The names googol and googolplex inspired the name of the Internet company Google and its corporate headquarters, the Googleplex, respectively.

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.

{| class="wikitable sortable" style="margin:0 auto;"

! Base <br />(short scale)

! Base <br />(long scale)

! Value

! US, Canada, and modern British<br />(short scale)

! Traditional British<br />(long scale)

! Traditional European<br />(Peletier long scale)

|-

| 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

| novendecillion

| 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

<!-- -->