Extensions of The Standard Dictionary Numbers
This table 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): 1,000,000 = 1 million; 1,000,0002 = 1 billion; 1,000,0003 = 1 trillion; 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, oddly enough, was also adapted from French usage but at a later date), and modern British usage, assigns new names for each power of one thousand (the short scale.) Thus, a billion is 1000 × 10002 = 109; a trillion is 1000 × 10003 = 1012; 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 been using the short scale, reverted to the long scale.
The term milliard is unambiguous and always means 109. 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.
With regard to 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 "Milliarde" in German, "miljard" in Dutch, "milyar" in Turkish and "миллиард" 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 (short scale) or 106n (long scale) and concatenating Latin roots for its units, tens, and hundreds place, together with the suffix -illion. In this way, numbers up to 103·999+3 = 103000 (short scale) or 106·999 = 105994 (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:
units | tens | hundreds | |
---|---|---|---|
1 | un | n deci | nx centi |
2 | duo | ms viginti | n ducenti |
3 | tre (*) | ns triginta | ns trecenti |
4 | quattuor | ns quadraginta | ns quadringenti |
5 | quinqua | ns quinquaginta | ns quingenti |
6 | se (*) | n sexaginta | n sescenti |
7 | septe (*) | n septuaginta | n septingenti |
8 | octo | mx octoginta | mx octingenti |
9 | nove (*) | nonaginta | nongenti |
- (*) ^ When preceding a component marked s or x, “tre” increases to “tres” and “se” to “ses” or “sex”; similarly, when preceding a component marked m or n, “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 106,000,258, 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.
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 and long and short scales.
Base -illion (short scale) |
Value | U.S. and modern British (short scale) |
Traditional British (long scale) |
Traditional European (Peletier) (long scale) |
SI Symbol |
SI Prefix |
---|---|---|---|---|---|---|
1 | 106 | Million | Million | Million | M | mega- |
2 | 109 | Billion | Thousand million | Milliard | G | giga- |
3 | 1012 | Trillion | Billion | Billion | T | tera- |
4 | 1015 | Quadrillion | Thousand billion | Billiard | P | peta- |
5 | 1018 | Quintillion | Trillion | Trillion | E | exa- |
6 | 1021 | Sextillion | Thousand trillion | Trilliard | Z | zetta- |
7 | 1024 | Septillion | Quadrillion | Quadrillion | Y | yotta- |
8 | 1027 | Octillion | Thousand quadrillion | Quadrilliard | ||
9 | 1030 | Nonillion | Quintillion | Quintillion | ||
10 | 1033 | Decillion | Thousand quintillion | Quintilliard | ||
11 | 1036 | Undecillion | Sextillion | Sextillion | ||
12 | 1039 | Duodecillion | Thousand sextillion | Sextilliard | ||
13 | 1042 | Tredecillion | Septillion | Septillion | ||
14 | 1045 | Quattuordecillion | Thousand septillion | Septilliard | ||
15 | 1048 | Quindecillion | Octillion | Octillion | ||
16 | 1051 | Sedecillion | Thousand octillion | Octilliard | ||
17 | 1054 | Septendecillion | Nonillion | Nonillion | ||
18 | 1057 | Octodecillion | Thousand nonillion | Nonilliard | ||
19 | 1060 | Novendecillion | Decillion | Decillion | ||
20 | 1063 | Vigintillion | Thousand decillion | Decilliard | ||
21 | 1066 | Unvigintillion | Undecillion | Undecillion | ||
22 | 1069 | Duovigintillion | Thousand undecillion | Undecilliard | ||
23 | 1072 | Tresvigintillion | Duodecillion | Duodecillion | ||
24 | 1075 | Quattuorvigintillion | Thousand duodecillion | Duodecilliard | ||
25 | 1078 | Quinquavigintillion | Tredecillion | Tredecillion | ||
26 | 1081 | Sesvigintillion | Thousand tredecillion | Tredecilliard | ||
27 | 1084 | Septemvigintillion | Quattuordecillion | Quattuordecillion | ||
28 | 1087 | Octovigintillion | Thousand quattuordecillion | Quattuordecilliard | ||
29 | 1090 | Novemvigintillion | Quindecillion | Quindecillion | ||
30 | 1093 | Trigintillion | Thousand quindecillion | Quindecilliard | ||
31 | 1096 | Untrigintillion | Sedecillion | Sedecillion | ||
32 | 1099 | Duotrigintillion | Thousand sedecillion | Sedecilliard | ||
33 | 10102 | Trestrigintillion | Septendecillion | Septendecillion | ||
34 | 10105 | Quattuortrigintillion | Thousand septendecillion | Septendecilliard | ||
35 | 10108 | Quinquatrigintillion | Octodecillion | Octodecillion | ||
36 | 10111 | Sestrigintillion | Thousand octodecillion | Octodecilliard | ||
37 | 10114 | Septentrigintillion | Novendecillion | Novendecillion | ||
38 | 10117 | Octotrigintillion | Thousand novendecillion | Novendecilliard | ||
39 | 10120 | Noventrigintillion | Vigintillion | Vigintillion | ||
40 | 10123 | Quadragintillion | Thousand vigintillion | Vigintilliard | ||
50 | 10153 | Quinquagintillion | Thousand quinquavigintillion | Quinquavigintilliard | ||
60 | 10183 | Sexagintillion | Thousand trigintillion | Trigintilliard | ||
70 | 10213 | Septuagintillion | Thousand quinquatrigintillion | Quinquatrigintilliard | ||
80 | 10243 | Octogintillion | Thousand quadragintillion | Quadragintilliard | ||
90 | 10273 | Nonagintillion | Thousand quinquaquadragintillion | Quinquaquadragintilliard | ||
100 | 10303 | Centillion | Thousand quinquagintillion | Quinquagintilliard | ||
101 | 10306 | Uncentillion | Unquinquagintillion | Unquinquagintillion | ||
102 | 10309 | Duocentillion | Thousand unquinquagintillion | Unquinquagintilliard | ||
103 | 10312 | Trescentillion | Duoquinquagintillion | Duoquinquagintillion | ||
110 | 10333 | Decicentillion | Thousand quinquaquinquagintillion | Quinquaquinquagintilliard | ||
111 | 10336 | Undecicentillion | Sesquinquagintillion | Sesquinquagintillion | ||
120 | 10363 | Viginticentillion | Thousand sexagintillion | Sexagintilliard | ||
121 | 10366 | Unviginticentillion | Unsexagintillion | Unsexagintillion | ||
130 | 10393 | Trigintacentillion | Thousand quinquasexagintillion | Quinquasexagintilliard | ||
140 | 10423 | Quadragintacentillion | Thousand septuagintillion | Septuagintilliard | ||
150 | 10453 | Quinquagintacentillion | Thousand quinquaseptuagintillion | Quinquaseptuagintilliard | ||
160 | 10483 | Sexagintacentillion | Thousand octogintillion | Octogintilliard | ||
170 | 10513 | Septuagintacentillion | Thousand quinquaoctogintillion | Quinquaoctogintilliard | ||
180 | 10543 | Octogintacentillion | Thousand nonagintillion | Nonagintilliard | ||
190 | 10573 | Nonagintacentillion | Thousand quinquanonagintillion | Quinquanonagintilliard | ||
200 | 10603 | Ducentillion | Thousand centillion | Centilliard | ||
300 | 10903 | Trecentillion | Thousand quinquagintacentillion | Quinquagintacentilliard | ||
400 | 101203 | Quadringentillion | Thousand ducentillion | Ducentilliard | ||
500 | 101503 | Quingentillion | Thousand quinquagintaducentillion | Quinquagintaducentilliard | ||
600 | 101803 | Sescentillion | Thousand trecentillion | Trecentilliard | ||
700 | 102103 | Septingentillion | Thousand quinquagintatrecentillion | Quinquagintatrecentilliard | ||
800 | 102403 | Octingentillion | Thousand quadringentillion | Quadringentilliard | ||
900 | 102703 | Nongentillion | Thousand quinquagintaquadringentillion | Quinquagintaquadringentilliard | ||
1000 | 103003 | Millinillion | Thousand quingentillion | Quingentilliard |
Value | U.S. and modern British (short scale) |
Traditional British (long scale) |
Traditional European (Peletier) (long scale) |
---|---|---|---|
10100 | Googol (Ten duotrigintillion) | Googol (Ten thousand sedecillion) | Googol (Ten sedecilliard) |
Googolplex | Googolplex | Googolplex |
Read more about this topic: Names Of Large Numbers
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