# Number names

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). Britain and Australia have recently largely switched from the European to the American system. 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.

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.

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.
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.

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
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

Compare to Chinese numerals