Numeral (linguistics)
Some English (finite) cardinal numbers
There are two main English language systems of naming numbers: the American system (also used in Canada) and the European system (used in most Germanic and Romanic languages). The European system is the older one and was also called the British system, because it was used in Great Britain. Britain and Australia have recently largely switched to the American system.
The British system is the older system, and its cognates are still used in European languages other than English. The American system was originally invented by the French, adopted by the United States, and then abandoned by France.
In the European system a billion is a million million, a trillion is a million billion, and so forth; a thousand billion is called a billiard, a thousand trillion a trilliard etc. In the American system a billion is a thousand million, a trillion is a thousand million, and so forth. See more below.
- Zero
- One fr.
- Two fr. Old English twa
- Three
- Four
- Five
- Six
- Seven
- Eight
- Nine
- Ten
- Eleven
- Twelve fr. Old English twelf
- Thirteen
- Fourteen
- Fifteen
- Sixteen
- Seventeen
- Eighteen
- Nineteen
- Twenty fr. Old English twegentig
- Thirty
- Forty
- Fifty
- Sixty
- Seventy
- Eighty
- Ninety
- Hundred
- Thousand
- Myriad
- Million
- Milliard
- Billion
- Trillion
- Quadrillion
- Quintillion
- Sextillion
- Septillion
- Octillion
- Nonilllion
- Decillion
- Undecillion
- Duodecillion
- Tredecillion
- Quattuordecillion
- Quindecillion
- Sexdecillion
- Septendecillion
- Octodecillion
- Novemdecillion
- Vigintillion
- Googol
- Centillion
- Googolplex
After the million mark, the European number systems is based on millions, the American number system is based on thousands. The prefix of the number name corresponds to the power of the base number. e.g. bi means 2; tri means 3 etc. or (n)illion = millionn or 10n×6.
In the European system, each number is a power of a million, e.g.
one billion = (one million)2 or 1012;
one trillion = (one million)3 or 1018;
one quadrillion = (one million)4 or 1024;
one quintillion = (one million)5 or 1030;
one sextillion = (one million)6 or 1036;
one septillion = (one million)7 or 1042;
one octillion = (one million)8 or 1048;
one nonillion = (one million)9 or 1054;
one decillion = (one million)10 or 1060;
one undecillion = (one million)11 or 1066;
one duodecillion = (one million)12 or 1072;
one tredecillion = (one million)13 or 1078;
one quattuordecillion = (one million)14 or 1084;
one quindecillion = (one million)15 or 1090;
one sexdecillion = (one million)16 or 1096;
one septendecillion = (one million)17 or 10102;
one octodecillion = (one million)18 or 10108;
one novemdecillion = (one million)19 or 10114;
one vigintillion = (one million)20 or 10120;
...
one centillion = (one million)100 or 10 600.
In the American system, each number is a power of a thousand (the prefix and the number of power will match only when the first 1000 is factored out), e.g.
(n)illion = 1000 × 1000n or 10(n+1)×3.
one billion = 1000 * 10002 or 109;
one trillion = 1000 * 10003 or 1012;
one quadrillion = 1000 * 10004 or 1015;
one quintillion = 1000 * 10005 or 1018;
one sextillion = 1000 * 10006 or 1021;
one septillion = 1000 * 10007 or 1024;
one octillion = 1000 * 10008 or 1027;
one nonillion = 1000 * 10009 or 1030;
one decillion = 1000 * 100010 or 1033;
one undecillion = 1000 * 100011 or 1036;
one duodecillion = 1000 * 100012 or 1039;
one tredecillion = 1000 * 100013 or 1042;
one quattuordecillion = 1000 * 100014 or 1045;
one quindecillion = 1000 * 100015 or 1048;
one sexdecillion = 1000 * 100016 or 1051;
one septendecillion = 1000 * 100017 or 1054;
one octodecillion = 1000 * 100018 or 1057;
one novemdecillion = 1000 * 100019 or 1060;
one vigintillion = 1000 * 100020 or 1063;
...
one centillion = 1000 * 1000100 or 10 303.
For more information on prefixes, see SI prefix.
See also Cardinal number and Natural number
In many Asian languages, the great redundancy of English number words is avoided.
Example: Japanese language (Some numbers have multiple names. Here, I give no more than one name for a number.)
| Number | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 100 | 1000 |
| Character | 零 | 一 | 二 | 三 | 四 | 五 | 六 | 七 | 八 | 九 | 十 | 百 | 千 |
| Name | rei | ichi | ni | san | yon | go | roku | nana | hachi | kyuu | juu | hyaku | sen |
Intermediate numbers are made by combining these elements:
Tens from 20 to 90 are "(digit)-juu".
Hundreds from 200 to 900 are "(digit)-hyaku".
Thousands from 2000 to 9000 are "(digit)-sen".
There are some phonetic modifications to larger numbers, but they are a minor detail.
In large numbers, elements are combined from largest to smallest, and zeros are implied.
11 = juu-ichi
17 = juu-nana
151 = hyaku-go-juu-ichi
302 = sam-byaku-ni
469 = yon-hyaku-roku-juu-kyuu
2025 = ni-sen-ni-juu-go
Now the main point: REALLY big numbers are made in a manner nearly identical to that in English, EXCEPT they use groups for four digits:
RankCharacterName| 104 | 108 | 1012 |
| 万 | 億 | 兆 |
| man | oku | chou |
Examples: (spacing by groups of four digits is given only for clarity of explanation)
1`0000 = ichi-man
983`6703 = kyuu-hyaku-hachi-juu-san-man-roku-sen-nana-hyaku-san
20'3652'1801 = ni-juu-oku-san-zen-rop-pyaku-go-juu-ni-man-sen-hap-pyaku-ichi
Since Japanese language was heavily influenced by Chinese, Japanese numerals are identical to Chinese numerals except the difference in pronunciations.
A note on Indian numerals
History of Large Numbers
In the Western world specific names for larger numbers did not come into use until quite recently. The Ancient Greeks did not get further than ten thousand. The Romans expressed 1,000,000 as decies centena milia, that is, 'ten hundred thousand'; it was only in the 13th century that the (originally French) word 'million' was introduced .
However, the Indians, who also invented the positional number system and the zero, were much more advanced in this aspect than all the other civilisations of Antiquity and the Middle Ages. By the 7th century AD Indian mathematicians were familiar enough with the notion of infinity as to define it as the quantity whose denominator is zero.
This achievement can probably be explained by the Indians' passion for high numbers, which is intimately related to their religious thought. For example, in texts belonging to the Vedic literature which are dated around the third century AD we find individual Sanskrit names for each of the powers of 10 up to 1012. (Even today, the words 'lakh' and 'koti', referring to 100,000 and 10,000,000, respectively, are in common use among English-speaking Indians.)
The 'Lalitavistara Sutra' (a Mahayana buddhist work) recounts a contest including writing, arithmetic, wrestling and archery, in which the Buddha was pitted against the great mathematician Arjuna and showed off his numerical skills by citing the names of the powers of ten up to 1 'tallakshana', which equals 1053, but then going on to explain that this is just one of a series of counting systems that can be expanded geometrically. The last number at which he arrived after going through nine successive counting systems was 10421, that is, a 1 followed by 421 zeros.
It is interesting to note that there is also an analogous system of Sanskrit terms for fractional numbers, which shows the capacity to deal with both very high and very small numbers.
Reference: Georges Ifrah, The Universal History of Numbers, ISBN 186046324X