| Numeral systems by culture | |
|---|---|
| Hindu-Arabic numerals | |
| Western Arabic Eastern Arabic Khmer |
Indian family Brahmi Thai |
| East Asian numerals | |
| Chinese Suzhou Counting rods |
Japanese Korean Mongolian |
| Alphabetic numerals | |
| Abjad Armenian Cyrillic Ge'ez |
Hebrew Greek (Ionian) Āryabhaṭa |
| Other systems | |
| Attic Babylonian Egyptian English |
Etruscan Mayan Roman Urnfield |
| List of numeral system topics | |
| Positional systems by base | |
| Decimal (10) | |
| 2, 4, 8, 16, 32, 64 | |
| 1, 3, 9, 12, 20, 24, 30, 36, 60, more… | |
Chinese numerals are characters for writing numbers in Chinese. Today, speakers of Chinese use three numeral systems: the ubiquitous system of Arabic numerals, along with two ancient Chinese numeral systems.
One such system is the Suzhou numerals or huama system. It has gradually been supplanted by the Arabic system in writing numbers. It is the only surviving variation of the rod numeral system, was once popular in use only in Chinese markets, such as those in Hong Kong before the 1990s.
The other Chinese numeral system is the written numbers system. It is still in use when writing numbers in long form, such as on cheques to hinder forgery. This character system is roughly analogous to spelling out a number in English 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 for convenience.
Individual Chinese characters in this article link to their dictionary entries.
Contents |
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 numerals, in the same way that spelling out numbers in English does not.
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 叁拾 (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 financial), can be easily manipulated into 弍 (two) or 弎 (three). |
| 貳(T) or 贰(S) |
二 | 2 | èr | also 弍 (obsolete financial), can be easily manipulated into 弌 (one) or 弎 (three). also 兩(T) or 两(S), see Characters with regional usage section. |
| 叄(T) or 叁(S) |
三 | 3 | sān | also 弎 (obsolete financial), can be easily manipulated into 弌 (one) or 弍 (two). 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 or 仟. |
| 佰 | 百 | 100 | bǎi | |
| 仟 | 千 | 1,000 | qiān | |
| 萬 | 萬(T) or 万(S) |
104 | wàn | Chinese numbers group by ten-thousands see Reading and transcribing numbers section below. |
| 億 | 億(T) or 亿(S) |
108 | yì | See large numbers section below. |
| Financial | Normal | Value | Pinyin | Standard alternative | Notes |
|---|---|---|---|---|---|
| 么(T) or 幺(S) | 1 | yāo | 一 | Literally means "the smallest". It is used in mainland China to unambiguously pronounce "#1" in series of digits (such as phone numbers and ID numbers). It is never used in counting or reading values. In Taiwan, it is only used by soldiers, police, and emergency services. In Hong Kong and Macau, it is only used when communicating in Standard Mandarin. | |
| 兩(T) or 两(S) | 2 | liǎng | 二 | A very common alternative way of saying "two". Its usage varies from dialect to dialect, even person to person. For example "2222" can read as "二千二百二十二", "两千二百二十二" or even "两千两百二十二" in Mandarin. See Reading and transcribing numbers section below. | |
| 念 | 廿 | 20 | niàn | 二十 | The written form is still used to refer to dates, especially Chinese calendar dates. Spoken form is still used in various dialects of Chinese. See Reading and transcribing numbers section below. 卄 is a rare variant. |
| 卅 | 30 | sà | 三十 | The written form is still used to abbreviate date references in Chinese. For example, May 30 Movement (五卅运动). Spoken form is still used in various dialects of Chinese. See Reading and transcribing numbers section below. |
|
| 卌 | 40 | xì | 四十 | Spoken form is still used in various dialects of Chinese, albeit very rare. | |
| 皕 | 200 | bì | 二百 | Very rarely used, one common example is the literature 《皕宋楼》. |
Similar to the long and short scales in the west, for numeral characters greater than 万 (wàn), there have been four systems in ancient and modern usage:
| System | 亿 yì |
兆 zhào |
京 jīng |
垓 gāi |
秭 zǐ |
穰 ráng |
沟 gōu |
涧 jiàn |
正 zhēng |
载 zài |
Factor of increase |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Alternative | 經/经 | 杼 | 壤 | ||||||||
| 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 (万 wàn) times the previous. |
| 3 | 108 | 1016 | 1024 | 1032 | 1040 | 1048 | 1056 | 1064 | 1072 | 1080 | Each numeral is 108 (万万 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. 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. However, most people do not recognize numerals beyond 亿 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).
One example of ambiguity is 兆zhào, which traditionally means 1012 but is also used for 106 in information technology in recent years (esp. in mainland China). To avoid problems arising from the ambiguity, the PRC government never uses this character in official documents, but uses 万亿wànyì instead. (On the other hand, the ROC government in Taiwan uses 兆zhào to mean 1012 in official documents.)
The numerals beyond 载 zài come from Buddhist texts in Sanskrit, but these "Buddhist numerals" have become "ancient usage".
| Name | Value | Notes |
|---|---|---|
| 極(T) or 极(S) |
1048 | |
| 恒河沙 | 1052 | Literally means "Sands of the Ganges", a metaphor used in number of Buddhist texts to convey a quantity equal to the number of grains of sand in the Ganges river. |
| 阿僧祇 | 1056 | From Sanskrit Asaṃkhyeya |
| 那由他 | 1060 | From Sanskrit Nayuta |
| 不可思議(T) or 不可思议(S) |
1064 | Literally translated as "unfathomable" or "unthinkable". |
| 無量(T) or 无量(S) |
1068 | Literally translated "without limit" |
| 大數(T) or 大数(S) |
1072 | Literally translated "big number" |
The following are characters used to denote small order of magnitude in Chinese historically. With the introduction of SI units, some of them have been incorporated as SI prefixes, while the rest has fallen into disuse.
| Character | Value | Notes |
|---|---|---|
| 漠 | 10-12 | (Ancient Chinese) 皮 corresponds the SI prefix pico. |
| 渺 | 10-11 | (Ancient Chinese) |
| 埃 | 10-10 | (Ancient Chinese) |
| 尘 | 10-9 | (Ancient Chinese) 奈 (T) or 纳 (S) corresponds the SI prefix nano. |
| 沙 | 10-8 | (Ancient Chinese) |
| 纤 | 10-7 | (Ancient Chinese) |
| 微 | 10-6 | still in use, corresponds the SI prefix micro. |
| 忽 | 10-5 | (Ancient Chinese) |
| 丝 | 10-4 | (Ancient Chinese) |
| 毫 | 1/1,000 | also 毛. still in use, corresponds the SI prefix milli. |
| 厘 | 1/100 | also 釐. still in use, corresponds the SI prefix centi. |
| 分 | 1/10 | still in use, corresponds the SI prefix deci. |
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, 纤, 沙, 尘, 渺) were defined as translations for the SI prefixes. For instance, 京 jīng was defined as giga, and 纤 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, Taiwanese defined 百万 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 | 纤 xiān | 纳 nà | 奈 nài |
| 10-12 | p | pico | 沙 shā | 皮 pí | 皮 pí |
| 10-15 | f | femto | 尘 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 |
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 两 (liǎng) is used rather than 二 (èr) for all numbers greater than 200 with the "2" numeral. Use of both 两 (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), 两 (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 两百 | 二百 or 两百 | 两百 | 两百 |
| 2000 | [2] (liǎng) [1000] | 二千 or 两千 | 二千 or 两千 | 两千 | 两千 |
| 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] | 两千三百六十二 | 二千三百六十二 | 两千三百六十二 | 两千三百六十二 |
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] | 一万两千 | [1] [10000] [2] or [10000] [2] |
一万二 or 万二 |
| 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:
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 (万) = yì (亿). 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) | 十二万三千四百五十六亿七千八百九十万两千三百四十五 |
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] [10,000] [0] [4] | 十万〇四 |
| 10,050,026 (1005,0026) |
(1005) [10,000] (26) or (1005) [10,000] (026) |
一千〇五万〇二十六 or 一千〇五万二十六 |
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] | 一十六点九八 |
| 12345.6789 | [1] [10000] [2] [1000] [3] [100] [4] [10] [5] [point] [6] [7] [8] [9] | 一万两千三百四十五点六七八九 |
| 75.4025 | [7] [10] [5] [point] [4] [0] [2] [5] | 七十五点四〇二五 |
| 0.1 | [0] [point] [1] | 〇点一 |
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 are formed by adding 負 (traditional) 负 (simplified) ("negative") before the number.
| Number | Structure | Characters |
|---|---|---|
| -1158 | [negative] [1] [1000] [1] [100] [5] [10] [8] | 负一千一百五十八 |
| -3 5/6 | [negative] [3] [again] [6] [parts of] [5] | 负三又六分之五 |
| -75.4025 | [negative] [7] [10] [5] [point] [4] [0] [2] [5] | 负七十五点四〇二五 |
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 (苏州) or huāmǎ (花码) 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.
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.
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.