Chinese numerals
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Chinese numerals are characters for writing numbers in Chinese. Today, speakers of Chinese use three numeral systems: the ubiquitous system of Arabic numeral system, along with two ancient Chinese numeral systems. The Suzhou numerals (simplified Chinese: 苏州码子; traditional Chinese: 蘇州碼子; pinyin: Sūzhōu mǎzi) or huama (simplified Chinese: 花码; traditional Chinese: 花碼; pinyin: huāmǎ; lit. 'flowery or fancy numbers') system has gradually been supplanted by the Arabic system in writing numbers. The character system is still used and roughly analogous to writing out a number in text. The Chinese character system can be classified as part of the language, but it still counts as a number system. Most people in China now use the Arabic system.
The huama system, the only surviving variation of the rod numeral system, was once popular in use only in Chinese markets (e.g. in Hong Kong, before 1990). The character writing system is still in use when writing numbers in long form, such as on cheques to hinder 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 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 Arabic numeralss, in the same way that spelling out numbers in English does not.
Numeral characters
There are 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. A forger could easily change everyday characters 三十 (30) to 五千 (5000) by adding just a few strokes. That would not be possible when writing using the financial characters 叄拾 (30) and 伍仟 (5000).
S denotes Simplified, T denotes Traditional
| Financial | Normal | Value | Pīnyīn | Notes |
|---|---|---|---|---|
| 零 | 〇 | 0 | líng | 〇 is an informal way to represent zero, but 零 is more commonly used, especially in schools. |
| 壹 | 一 | 1 | yī | also 弌 (obsolete) also 么(T) or 幺(S) yāo when used in phone numbers etc., see footnote 1. |
| 貳(T) or 贰(S) |
二 | 2 | èr | also 弍 (obsolete) also 兩(T) or 两(S) liǎng when used when placed before a measure word. |
| 叄(T) or 叁(S) |
三 | 3 | sān | also 弎 (obsolete) also 參(T) or 参(S) sān. |
| 肆 | 四 | 4 | sì | |
| 伍 | 五 | 5 | wǔ | |
| 陸(T) or 陆(S) |
六 | 6 | liù | |
| 柒 | 七 | 7 | qī | |
| 捌 | 八 | 8 | bā | |
| 玖 | 九 | 9 | jiǔ | |
| 拾 | 十 | 10 | shí | Although some people use 什 as financial, it is not acceptable because it can be written over into 伍. |
| 念 or 貳拾 |
廿 or 卄 |
20 | niàn | 卄 was rarely used, but still frequently used in spoken Chinese both used mostly on calendars (二十 is used). see constructing numbers below. |
| 叄拾 | 卅 | 30 | sà | 卅 was rarely used, but still frequently used in spoken Chinese used mostly on calendars (三十 is used). |
| 肆拾 | 卌 | 40 | xì | 卌 was hardly used (四十 is used). |
| 佰 | 百 | 100 | bǎi | |
| 仟 | 千 | 1,000 | qiān | |
| 萬 | 萬(T) or 万(S) |
104 | wàn | Chinese numbers group by ten-thousands see constructing numbers below. |
| 億 | 億(T) or 亿(S) |
108 | yì
Also: 105. | |
| 兆 | 1012 | zhào
Also: 106, 1016. | ||
| 京 | 1016 | jīng | (Ancient Chinese) Also: 107, 1024, 1032. | |
| 垓 | 1020 | gāi | (Ancient Chinese) Also: 108, 1032, 1064. | |
| 秭 | 1024 | zǐ | (Ancient Chinese) Also: 109, 1040, 10128. | |
| 穰 | 1028 | ráng | (Ancient Chinese) Also: 1010, 1048, 10256. also 壤. | |
| 溝(T) or 沟(S) |
1032 | gōu | (Ancient Chinese) Also: 1011, 1056, 10512. | |
| 澗(T) or 涧(S) |
1036 | jiàn | (Ancient Chinese) Also: 1012, 1064, 101024. | |
| 正 | 1040 | (Ancient Chinese) Also: 1013, 1072, 102048. | ||
| 載(T) or 载(S) |
1044 | (Ancient Chinese) Also: 1014, 1080, 104096. | ||
| 極(T) or 极(S) |
1048 | jí | (Buddhism) | |
| 恒河沙 | 1052 | (Buddhism) The 3-character expression means roughly "Sand of the Ganges" and also appears in a Buddhist sutra; it is used in that context to convey a quantity equal to the number of grains of sand in the said river. | ||
| 阿僧祇 | 1056 | (Buddhism) | ||
| 那由他 | 1060 | (Buddhism) | ||
| 不可思議(T) or 不可思议(S) |
1064 | (Buddhism) Literally translated as "unfathomable" or "unthinkable". | ||
| 無量(T) or 无量(S) |
1068 | (Buddhism) Literally translated "without limit" | ||
| 大數(T) or 大数(S) |
1072 | (Buddhism) Literally translated "big number" | ||
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, etc. 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).
| Character | Value | Notes |
|---|---|---|
| 漠 | 10-12 | (Ancient Chinese) |
| 渺 | 10-11 | (Ancient Chinese) |
| 埃 | 10-10 | (Ancient Chinese) |
| 塵 | 10-9 | (Ancient Chinese) |
| 沙 | 10-8 | (Ancient Chinese) |
| 纖 | 10-7 | (Ancient Chinese) |
| 微 | 10-6 | still in use, corresponds the SI prefix micro. |
| 忽 | 10-5 | (Ancient Chinese) |
| 絲 | 10-4 | (Ancient Chinese) |
| 毫 | 1/1,000 | also 毛. |
| 厘 | 1/100 | also 釐. |
| 分 | 1/10 | still in use, 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 or 兩百 | 兩百 | 兩百 |
| 2000 | [2] (liǎng) [1000] | 兩千 | 二千 or 兩千 | 兩千 | 兩千 |
| 45 | [4] [10] [5] | 四十五 | 四十五 or 卌五 | 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.
In certain older texts like the Protestant Bible or in poetic usage, numbers such as 114 may be written as [100] [10] [4] (百十四).
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] | 二百零五 |
| 100,004 (10,0004) |
[10] [10,000] [0] [4] | 十萬零四 |
| 10,050,026 (1005,0026) |
(1005) [10,000] (26) or (1005) [10,000] (026) |
一千零五萬零二十六 or 一千零五萬二十六 |
Large number systems
For numeral characters greater than 萬 (wàn), there have been four systems in ancient and modern usage:
| System | 億 yì |
兆 zhào |
京 jīng |
垓 gāi |
秭 zǐ |
穰 ráng |
溝 gōu |
澗 jiàn |
正 zhēng |
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. |
In modern Chinese, only the second system is used in expressing numbers[citation needed]. Although there is some dispute on the value of 兆 zhào, the usage (representing 1012) is still consistent through Chinese communities, as well as Japan, Korea[citation needed]. However, most people do not recognize numerals beyond 億 yì (108) and dictionary definitions on the words of larger number may not be consistent (except Korea where 兆zhào and 京jīng are frequently used) The numerals beyond 載 jí come from Buddhist texts in Sanskrit, but these "Buddhist numerals" have become "ancient usage".
Fractional values
To construct a fraction, the denominator is written first, followed by 分之 ("parts of") and then the numerator. This is the opposite of how fractions are read in English, which is numerator first. Each half of the fraction is written the same as a whole number. Mixed numbers are written with the whole-number part first, followed by 又 ("again"), then the fractional part.
| Fraction | Structure | Characters |
|---|---|---|
| 2/3 | [3] [parts of] [2] | 三分之二 |
| 15/32 | [3] [10] [2] [parts of] [10] [5] | 三十二分之十五 |
| 1/3000 | [3] [1000] [parts of] [1] | 三千分之一 |
| 3 5/6 | [3] [again] [6] [parts of] [5] | 三又六分之五 |
Percentages are constructed similarly, using 百 (100) as the denominator. The 一 (one) before 百 is omitted.
| Percentage | Structure | Characters |
|---|---|---|
| 25% | [100] [parts of] [2] [10] [5] | 百分之二十五 |
| 110% | [100] [parts of] [1] [100] [1] [10] | 百分之一百一十 |
Decimal numbers are constructed by first writing the whole number part, then inserting 點 (traditional) or 点 (simplified) ("point"), and finally the decimal expression. The decimal expression is written using only the digits for 0 to 9, without multiplicative words.
| Decimal expression | Structure | Characters |
|---|---|---|
| 16.98 | [10] [6] [point] [9] [8] | 一十六點九八 |
| 12345.6789 | [1] [10000] [2] [100] [4] [10] [5] [point] [6] [7] [8] [9] | 一萬兩千三百四十五點六七八九 |
| 75.4025 | [7] [10] [5] [point] [4] [0] [2] [5] | 七十五點四零二五 |
| 0.1 | [0] [point] [1] | 零點一 |
Ordinal numbers
Ordinal numbers are formed by adding 第 ("sequence") before the number.
| Ordinal | Structure | Characters |
|---|---|---|
| 1st | [sequence] [1] | 第一 |
| 2nd | [sequence] [2] | 第二 |
| 82nd | [sequence] [8] [10] [2] | 第八十二 |
Negative numbers
Negative numbers are formed by adding 負 (traditional) 负 (simplified) ("negative") before the number.
| Number | Structure | Characters |
|---|---|---|
| -1158 | [negative] [1] [1000] [1] [100] [5] [10] [8] | 負一千一百五十八 |
| -3 5/6 | [negative] [3] [again] [6] [parts of] [5] | 負三又六分之五 |
| -75.4025 | [negative] [7] [10] [5] [point] [4] [0] [2] [5] | 負七十五點四零二五 |
SI prefixes
The translations for the SI prefixes in earlier days were different from those used today. The larger (兆, 京, 垓, 秭, 穰), and smaller Chinese numerals (微, 纖, 沙, 塵, 渺) were defined as translations for the SI prefixes. For instance, 京 jīng was defined as giga, and 纖 xiān was defined as nano. This resulted in the creation of more values for each numeral.
By the time of "early translation", a dispute had arisen over the value of 兆 . The government of the PRC used a part of this translation, and defined 兆 zhào as the translation for the SI prefix mega (106). (Perhaps the government was not aware of the common usage of 兆, and thus did not consider an alternative single Chinese character, such as 巨, to represent mega.) Because of this, the translation has caused much confusion.
In addition, the Taiwanese government defined 百萬 as the translation for mega. This translation is widely used in official documents, academic communities, informational industries, etc. However, the civil broadcasting industries sometimes use 兆赫 to represent "megahertz".
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 SI prefixes. However, the governments have each chosen different Chinese characters for certain prefixes. 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 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 Suzhou (蘇州) or huāmǎ (花碼) system is a variation of the Southern Song rod numerals. Nowadays, the huāmǎ system is only used for displaying prices in Chinese markets or on traditional handwritten invoices.
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.
Cultural influences
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.