Chinese numerals
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The huama system, the only surviving variation of the rod numeral system, is nowadays in use only in Chinese markets (e.g. in Hong Kong). The character writing system is still in use when writing numbers in long form such as on cheques, as their complexity thwarts forgery.
Individual Chinese characters in this article link to their dictionary entries.
Written numbers
The Chinese character numeral system consists of the Chinese characters used by the Chinese written language to write spoken numerals. Similarly to spelled-out numbers in English (e.g., "one thousand nine hundred [and] forty-five"), it is not an independent system per se. And since it reflects spoken language, it does not use the positional system as is done in Hindu-Arabic numerals, in the same way that spelling out numbers in English does not.Numeral characters
There are ten characters representing the numbers zero through nine, and other characters representing larger numbers such as tens, hundreds, thousands and so on. There are two sets of characters for Chinese numerals: one for everyday writing and one for use in commercial or financial contexts known as dàxiě (大寫 in traditional Chinese, 大写 in simplified Chinese). The latter arose because the characters used for writing numerals are geometrically simple, so simply using those numerals cannot prevent forgeries in the same way spelling numbers out in English would.S denotes Simplified, T denotes Traditional.
| Pinyin | Financial | Normal | Value | Notes |
|---|---|---|---|---|
| líng | [[wikt:零|零]] | [[wikt:〇|〇]] | 0 | 〇 is a informal way to represent zero, but sometimes 零 is the way, too. Many people don't use 〇. |
| yī | [[wikt:壹|壹]] | [[wikt:一|一]] | 1 | also 弌 (obsolete) also 么(T) or 幺(S) yāo when used in phone numbers etc., see footnote 1. |
| èr | [[wikt:貳|貳]](T) or 贰(S) | [[wikt:二|二]] | 2 | also 弍 (obsolete) also 兩(T) or 两(S) liǎng when used when placed before a measure word. |
| sān | [[wikt:叄|叄]](T) or 叁(S) | [[wikt:三|三]] | 3 | also 弎 (obsolete) also 參(T) or 参(S) sān. |
| sì | [[wikt:肆|肆]] | [[wikt:四|四]] | 4 | |
| wǔ | [[wikt:伍|伍]] | [[wikt:五|五]] | 5 | |
| liù | [[wikt:陸|陸]] | [[wikt:六|六]] | 6 | |
| qī | [[wikt:柒|柒]] | [[wikt:七|七]] | 7 | |
| bā | [[wikt:捌|捌]] | [[wikt:八|八]] | 8 | |
| jiǔ | [[wikt:玖|玖]] | [[wikt:九|九]] | 9 | |
| shí | [[wikt:拾|拾]] | [[wikt:十|十]] | 10 | Although some people use 什, It is not acceptable because it can be written over into 伍. |
| niàn | 念 or 貳拾 | 廿 or 卄 | 20 | 卄 was rarely used, both used mostly on calendars (二十 is used). see constructing numbers below. |
| sà | 叄拾 | 卅 | 30 | 卅 was rarely used, used mostly on calendars (三十 is used). |
| xì | 肆拾 | 卌 | 40 | 卌 was rarely used (四十 is used). |
| bǎi | 佰 | 百 | 100 | |
| qiān | 仟 | 千 | 1,000 | |
| wàn | 萬 | 萬(T) or 万(S) | 104 | Chinese numbers group by ten-thousands see constructing numbers below. |
| yì | 億 | 億(T) or 亿(S) | 108 | (Ancient Chinese) Also: 105. see large number systems below. |
| zhào | 兆 | 1012 | (Ancient Chinese) Also: 106, 1016. Its usage has a dispute, see SI prefixes below. | |
| jīng | 京 | 1016 | (Ancient Chinese) Also: 107, 1024, 1032. also 經(T) or 经(S) jīng. | |
| gāi | 垓 | 1020 | (Ancient Chinese) Also: 108, 1032, 1064. | |
| zǐ | 秭 | 1024 | (Ancient Chinese) Also: 109, 1040, 10128. also 杼 zhù. 佑 yòu(S) or 尧 yáo(T) corresponds the SI prefix yotta. | |
| ráng | 穰 | 1028 | (Ancient Chinese) Also: 1010, 1048, 10256. also 壤 rǎng. | |
| gōu | 溝(T) or 沟(S) | 1032 | (Ancient Chinese) Also: 1011, 1056, 10512. | |
| jiàn | 澗(T) or 涧(S) | 1036 | (Ancient Chinese) Also: 1012, 1064, 101024. | |
| zhèng | 正 | 1040 | (Ancient Chinese) Also: 1013, 1072, 102048. | |
| zài | 載(T) or 载(S) | 1044 | (Ancient Chinese) Also: 1014, 1080, 104096. | |
| jí | 極(T) or 极(S) | 1048 | (Ancient Chinese) | |
| 恒河沙 | 1052 | (Ancient Chinese) | ||
| 阿僧祇 | 1056 | (Ancient Chinese) | ||
| 那由他 | 1060 | (Ancient Chinese) | ||
| 不可思議 | 1064 | (Ancient Chinese) | ||
| 無量大數 | 1068 | (Ancient Chinese) | ||
么(T) or 幺(S) yāo, "the smallest", is used widely in mainland China as a replacement for yī in series of digits such as phone numbers, room numbers, et cetera, to prevent confusion between similar sounding words. It is never used in counting, nor is it used in Taiwan (except for soldiers in the ROC military, the police force, and the emergency telephone number 119 for calling a fire department or requesting an ambulance) or Hong Kong and Macau (except when communicating in Standard Mandarin).
| Pinyin | Financial | Normal | Value | Notes |
|---|---|---|---|---|
| mò | 漠 | 10-12 | (Ancient Chinese) 皮 pí corresponds the SI prefix pico. | |
| miǎo | 渺 | 10-11 | (Ancient Chinese) | |
| āi | 埃 | 10-10 | (Ancient Chinese) | |
| chén | 塵 | 10-9 | (Ancient Chinese) 奈 nài(T) or 纳 nà(S) corresponds the SI prefix nano. | |
| shā | 沙 | 10-8 | (Ancient Chinese) | |
| xiān | 纖 | 10-7 | (Ancient Chinese) | |
| wēi | 微 | 10-6 | also corresponds the SI prefix micro. | |
| hū | 忽 | 10-5 | (Ancient Chinese) | |
| sī | 絲 | 10-4 | (Ancient Chinese) | |
| háo | 毫 | 1/1,000 | also 毛 máo. also corresponds the SI prefix milli. | |
| lí | 厘 | 1/100 | also 釐 lí. also corresponds the SI prefix centi. | |
| fēn | 分 | 1/10 | also corresponds the SI prefix deci. |
Constructing numbers
Multiple-digit numbers are constructed using a multiplicative principle; first the digit itself (from 1 to 9), then the place (such as 10 or 100); then the next digit.In Mandarin, the multiplier 兩 (liǎng) is used rather than 二 (èr) for all numbers greater than 200 with the "2" numeral. Use of both 兩 (liǎng) or 二 (èr) are acceptable for the number 200. When writing in the Cantonese dialect, 二 (yi6) is used to represent the "2" numeral for all numbers. In the southern Min dialect of Chaozhou (Teochew), 兩 (no6) is used to represent the "2" numeral in all numbers from 200 onwards. Thus:
| Number | Structure | Characters | |||
|---|---|---|---|---|---|
| Mandarin | Cantonese | Chaozhou | Shanghainese | ||
| 60 | [6] [10] | 六十 | 六十 | 六十 | 六十 |
| 20 | [2] [10] or [20] | 二十 | 二十 or 廿 | 二十 | 廿 |
| 200 | [2] (èr) or (liǎng) [100] | 二百 or 兩百 | 二百 | 兩百 | 兩百 |
| 2000 | [2] (liǎng) [1000] | 兩千 | 二千 | 兩千 | 兩千 |
| 45 | [4] [10] [5] | 四十五 | 四十五 | 四十五 | 四十五 |
| 2,362 | [2] [1,000] [3] [100] [6] [10] [2] | 兩千三百六十二 | 二千三百六十二 | 兩千三百六十二 | 兩千三百六十二 |
For the numbers 11 through 19, the leading "one" (一) is usually omitted. In some dialects, like Shanghainese, when there are only two significant digits in the number, the leading "one" and the trailing zeroes are omitted. Sometimes, the one before "ten" in the middle of a number, such as 213, is omitted. Thus:
| Number | Strict Putonghua | Colloquial or dialect usage | ||
|---|---|---|---|---|
| Structure | Characters | Structure | Characters | |
| 14 | [10] [4] | 十四 | ||
| 12000 | [1] [10000] [2] [1000] | 一萬二千 | [1] [10000] [2] or [10000] [2] | 一萬二 or 萬二 |
| 114 | [1] [100] [1] [10] [4] | 一百一十四 | [1] [100] [10] [4] | 一百十四 |
| 1158 | [1] [1000] [1] [100] [5] [10] [8] | 一千一百五十八 | See note 1 below | |
Notes:
- Nothing is ever omitted in large and more complicated numbers such as this.
For numbers larger than a myriad, the same grouping system used in English applies, except in groups of four places (myriads) rather than in groups of three (thousands). Hence it is more convenient to think of numbers here as in groups of four, thus 1,234,567,890 is regrouped here as 12,3456,7890. Larger than a myriad, each number is therefore four zeroes longer than the one before it, thus 10000 × wàn (萬) = yì (億), 10000 × yì (億) = zhào (兆). If one of the numbers is between 10 and 19, the leading "one" is omitted as per the above point. Hence (numbers in parentheses indicate that the number has been written as one number rather than expanded):
| Number | Structure | Characters |
|---|---|---|
| 12,345,678,902,345 (12,3456,7890,2345) | (12) [1,0000,0000,0000] (3456) [1,0000,0000] (7890) [1,0000] (2345) | 十二兆三千四百五十六億七千八百九十萬兩千三百四十五 |
Interior zeroes before the unit position (as in 1002) must be spelt explicitly. The reason for this is that trailing zeroes (as in 1200) are often omitted as shorthand, so ambiguity occurs. One zero is sufficient to resolve the ambiguity. Where the zero is before a digit other than the units digit, the explicit zero is not ambiguous and is therefore optional, but preferred. Thus:
| Number | Structure | Characters |
|---|---|---|
| 205 | [2] [100] [0] [5] | 二百〇五 |
| 100,004 (10,0004) | [10] [1,0000] [0] [4] | 十萬〇四 |
| 10,050,026 (1005,0026) | (1005) [1,0000] (26) or (1005) [1,0000] (026) | 一千〇五萬〇二十六 or 一千〇五萬二十六 |
Large number systems
For numeral characters greater than [[wikt:萬|萬]] (wàn), there have been four systems in ancient and modern usage:| System | [[wikt:億>億]] yì | [[wikt:兆>兆]] zhào | [[wikt:京>京]] jīng | [[wikt:垓>垓]] gāi | [[wikt:秭>秭]] zǐ | [[wikt:穰>穰]] ráng | [[wikt:溝>溝]] gōu | [[wikt:澗>澗]] jiàn | [[wikt:正>正]] zhēng | [[wikt:載>載]] zài | Factor of increase |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 105 | 106 | 107 | 108 | 109 | 1010 | 1011 | 1012 | 1013 | 1014 | Each numeral is 10 (十 shí) times the previous. |
| 2 | 108 | 1012 | 1016 | 1020 | 1024 | 1028 | 1032 | 1036 | 1040 | 1044 | Each numeral is 10,000 (萬 wàn) times the previous. |
| 3 | 108 | 1016 | 1024 | 1032 | 1040 | 1048 | 1056 | 1064 | 1072 | 1080 | Each numeral is 108 (萬萬 wànwàn) times the previous. |
| 4 | 108 | 1016 | 1032 | 1064 | 10128 | 10256 | 10512 | 101024 | 102048 | 104096 | Each numeral is the square of the previous. |
SI prefixes
The translation for the SI prefixes in the earlier days is different from that in today. The larger Chinese numerals (兆, 京, 垓, 秭, 穰), and the smaller Chinese numerals (微, 纖, 沙, 塵, 渺) were defined as the translation for the SI prefixes. For instance, 京 jīng was defined as giga, and 纖 xiān was defined as nano, resulting for creation of more values for each numeral.
By the "early translation", the dispute of 兆 is arisen. The PRC government used a part of this translation, and defined [[wikt:兆|兆]] zhào as the translation for the SI prefix mega (106). (Maybe the government do not recognize the common usage of 兆, and do not consider alternative single Chinese character, like [[wikt:巨|巨]], for representing mega. ) However, the translation has caused much confusion.
In addition, the Taiwan government defined 百萬 as the translation for mega. This translation is widely used by the officials, academic communities, informational industries, and etc. But the rarely exception is, the civil broadcasting industries sometime use 兆赫 for representing "mega Hertz".
Today, both the governments of the People's Republic of China (Mainland China, Hong Kong and Macau) and Republic of China (Taiwan) use phonetic transliterations for the prefixes. However, the governments choose different Chinese characters for some particular prefix. The following table lists the two different standards together with the early translation.
| Value | Symbol | English | Early translation | PRC standard | ROC standard |
|---|---|---|---|---|---|
| 1024 | Y | yotta | 尧 yáo | 佑 yòu | |
| 1021 | Z | zetta | 泽 zé | 皆 jiē | |
| 1018 | E | exa | 穰 ráng | 艾 ài | 艾 ài |
| 1015 | P | peta | 秭 zǐ | 拍 pāi | 拍 pāi |
| 1012 | T | tera | 垓 gāi | 太 tài | 兆 zhào |
| 109 | G | giga | 京 jīng | 吉 jí | 吉 jí |
| 106 | M | mega | 兆 zhào | 兆 zhào | 百萬 bǎiwàn |
| 103 | k | kilo | 千 qiān | 千 qiān | 千 qiān |
| 102 | h | hecta | 百 bǎi | 百 bǎi | 百 bǎi |
| 101 | da | deca | 十 shí | 十 shí | 十 shí |
| 10-1 | d | deci | 分 fēn | 分 fēn | 分 fēn |
| 10-2 | c | centi | 厘 lí | 厘 lí | 厘 lí |
| 10-3 | m | milli | 毫 háo | 毫 háo | 毫 háo |
| 10-6 | µ | micro | 微 wēi | 微 wēi | 微 wēi |
| 10-9 | n | nano | 纖 xiān | 纳 nà | 奈 nài |
| 10-12 | p | pico | 沙 shā | 皮 pí | 皮 pí |
| 10-15 | f | femto | 塵 chén | 飞 fēi | 飛 fēi |
| 10-18 | a | atto | 渺 miǎo | 阿 à | 阿 à |
| 10-21 | z | zepto | 仄 zè | 介 jiè | |
| 10-24 | y | yocto | 幺 yāo | 攸 yōu |
Suzhou (蘇州) or huāmǎ (花碼) numerals
In the same way that Roman numerals were standard in ancient and medieval Europe for mathematics and commerce, the Chinese formerly used the rod numerals, which is a positional system. The huāmǎ system is a variation of the rod numeral system. Rod numerals are closely related to the counting rods and the abacus, which is why the numeric symbols for 1, 2, 3, 6, 7 and 8 in the huāmǎ system are represented in a similar way as on the abacus.Nowadays, the huāmǎ system is only used for displaying prices in Chinese markets or on traditional handwritten invoices. According to the Unicode standard version 3.0, these characters are called Hangzhou style numerals. This indicates that it is not used only by Cantonese in Hong Kong. In the Unicode standard 4.0, an erratum was added which stated:
- The Suzhou numerals (Chinese su1 zhou1 ma3 zi) are special numeric forms used by traders to display the prices of goods. The use of "HANGZHOU" in the names is a misnomer.
In the huāmǎ system, special symbols are used for digits instead of the Chinese characters. The digits are positional. When written horizontally, the numerical value is written in two rows. For example:
- 〤〇〢二
- 拾元
When written vertically, the above example is written thus:
- 拾〤
- 元〇
- 〢
- 二
Zero is represented by a circle, probably the numeral '0', letter 'O' or character [[wikt:〇|〇]] may work well. Leading and trailing zeros are unnecessary in this system. Additional characters representing 10, 20, 30 and 40 exist: [[wikt:十|十]], [[wikt:卄|卄]], [[wikt:卅|卅]], [[wikt:卌|卌]].
For those who cannot see the Unicode glyphs in the web browser, here is an image with the appearance of these digits:
Note: 9 is a dot on top of a variant of the 〤 (4) symbol ([[wikt:〩|〩]],not represented in the image); this symbol looks like the Chinese character for "jiǔ ([[wikt:久|久]])", compare to the formal character '9' "jiǔ ([[wikt:玖|玖]])". (Some web browsers, e.g. IE 5.5, display this character incorrectly as the "fǎn wén", or reverse "wén" radical (夂 & 攵 & 夊 & 文), click [here] to see the correct graphic glyph.)
The digits 1 to 3 come in the vertical and horizontal version so that they can alternate if these digits are next to each other. The first digit usually use the vertical version. e.g. 21 is written as 〢一 instead of 〢〡 which can be confused with 3 (〣).
Hand gestures
There is a common method of using of one hand to signify the numbers one to ten. While the five digits on one hand can express the numbers one to five, six to ten have special signs that can be used in commerce or day-to-day communication.
Miscellaneous
During Ming and Qing dynasties (when Arabic numerals were first introduced into China), some Chinese mathematicians used Chinese numeral characters as positional system digits. After Qing dynasty, both the Chinese numeral characters and the Suzhou numerals were replaced by Arabic numerals in mathematical writings.Traditional Chinese numeric characters are also used in Japan and Korea. In vertical text (that is, read top to bottom), using characters for numbers is the norm, while in horizontal text, Arabic numerals are most common. Chinese numeric characters are also used in much the same formal or decorative fashion that Roman numerals are in Western cultures. Chinese numerals may appear together with Arabic numbers on the same sign or document.
External links
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