Chinese numerals
Template:Numeral systems Today, speakers of Chinese use three numeral systems: the ubiquitous system of Arabic numerals, along with two ancient Chinese numeral systems. The huama (Template:Zh-d-cp; U+82B1, U+78BC; 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 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 mentioned in this article can be looked up graphically in the Unihan database by using the following access URL: http://www.unicode.org/cgi-bin/GetUnihanData.pl?codepoint=UUUU, where UUUU is the Unicode code point. e.g. use 82B1 for 'huā'.
Contents
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 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. 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 | 零 | 零 or 〇 | 0 | casual form is a circle |
yī | 壹 | 一 | 1 | also 弌 (obsolete) also 么 (yāo) when used in phone numbers etc., see footnote 1 |
èr | 貳 | 二 | 2 | also 弍 (obsolete) 两 (S), 兩 (T) (liǎng) is used when placed before a measure word |
sān | 叄 | 三 | 3 | 弎 (obsolete) 參 is also acceptable. |
sì | 肆 | 四 | 4 | |
wǔ | 伍 | 五 | 5 | |
liù | 陸 | 六 | 6 | |
qī | 柒 | 七 | 7 | |
bā | 捌 | 八 | 8 | |
jiǔ | 玖 | 九 | 9 | |
shí | 拾 | 十 | 10 | |
niàn | 貳拾 | 廿 | 20 | also 卄 used mostly on calendars; otherwise 二十 is used. see constructing numbers below |
sà | 叄拾 | 卅 | 30 | used mostly on calendars (三十 is used) |
xì | 肆拾 | 卌 | 40 | rarely used (四十 is used) |
bǎi | 佰 | 百 | 100 | |
qiān | 仟 | 千 | 1,000 | |
wàn | 萬 | 万 (S) 萬 (T) |
10^{4} | Chinese numbers group by ten-thousands see constructing numbers below |
yì | 億 | 亿 (S) 億 (T) |
10^{8} | also means 10^{5} in some ancient contexts. see large number systems below |
zhào | 兆 | 10^{12} | also means 10^{6} or 10^{16} in some ancient contexts
also means mega | |
jīng | 京 (or 經) |
10^{16} | (Ancient Chinese) Also: 10^{7}, 10^{24}, 10^{32}. | |
gāi | 垓 | 10^{20} | (Ancient Chinese) Also: 10^{8}, 10^{32}, 10^{64}. | |
zǐ | 秭 | 10^{24} | (Ancient Chinese) Also: 10^{9}, 10^{40}, 10^{128}. | |
ráng | 穰 | 10^{28} | (Ancient Chinese) Also: 10^{10}, 10^{48}, 10^{256}. | |
gōu | 溝 | 10^{32} | (Ancient Chinese) Also: 10^{11}, 10^{56}, 10^{512}. | |
jiàn | 澗 | 10^{36} | (Ancient Chinese) Also: 10^{12}, 10^{64}, 10^{1024}. | |
zhèng | 正 | 10^{40} | (Ancient Chinese) Also: 10^{13}, 10^{72}, 10^{2048}. | |
zài | 載 | 10^{44} | (Ancient Chinese) Also: 10^{14}, 10^{80}, 10^{4096}. | |
jí | 極 | 10^{48} | (Ancient Chinese) Also: 10^{15}, 10^{88}, 10^{8192}. | |
fēn | 分 | 1/10 | also means deci as a prefix, see SI prefixes below | |
lí | 釐 | 厘 | 1/100 | also means centi |
háo | 毫 | 1/1,000 | also means milli | |
sī | 絲 | 10^{-4} | (Ancient Chinese) | |
hū | 忽 | 10^{-5} | (Ancient Chinese) | |
wēi | 微 | 10^{-6} | also means micro as a prefix, see SI prefixes below | |
xiān | 纖 | 10^{-7} | (Ancient Chinese) | |
shā | 沙 | 10^{-8} | (Ancient Chinese) | |
chén | 塵 | 10^{-9} | (Ancient Chinese) In SI units it is called 納 nà | |
āi | 埃 | 10^{-10} | (Ancient Chinese) | |
miǎo | 渺 | 10^{-11} | (Ancient Chinese) | |
mò | 漠 | 10^{-12} | (Ancient Chinese) |
幺; (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) or Hong Kong and Macau (except when communicating in Standard Mandarin).
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, for numbers with 2 greater than 200, the multiplier 两 (liǎng) rather than 二 (èr) is used. When writing in a Cantonese culture, 二 (yi^{6}) is used in all cases. Also, in the southern Min dialect of Chaozhou (Teochew), 两 (no^{6}) is used in all cases. Thus:
Number | Structure | Characters | ||
---|---|---|---|---|
Mandarin | Cantonese | Chaozhou | ||
60 | [6] [10] | 六十 | 六十 | 六十 |
200 | [2] (èr) [100] | 二百 | 二百 | 两百 |
2000 | [2] (liǎng) [1000] | 两千 | 二千 | 两千 |
45 | [4] [10] [5] | 四十五 | 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 |
For the numbers 11 through 19, the leading "one" (一) is omitted. In some dialects, when there are only two significant digits in the number, the leading "one" and the trailing zeroes are omitted – but this is grammatically incorrect. Sometimes, the one before "ten" in the middle of a number, such as 213, is omitted; this too is grammatically incorrect. Thus:
Number | Correct | Incorrect but common | ||
---|---|---|---|---|
Structure | Characters | Structure | Characters | |
14 | [10] [4] | 十四 | ||
12000 | [1] [10000] [2] [1000] | 一万二千 | [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 | (nothing is ever omitted in large 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 (万) = yì (亿), 10000 × yì (亿) = 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] [1,0000] [0] [4] | 十万〇四 |
10,050,026 (1005,0026) |
(1005) [1,0000] (26) or (1005) [1,0000] (026) |
一千〇五万〇二十六 or 一千〇五万二十六 |
Large number systems
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) |
Factor of increase |
---|---|---|---|---|---|---|---|
1 | 10^{5} | 10^{6} | 10^{7} | 10^{8} | 10^{9} | 10^{10} | Each numeral is 10 (十 shí) times the previous. |
2 | 10^{8} | 10^{12} | 10^{16} | 10^{20} | 10^{24} | 10^{28} | Each numeral is 10,000 (万 wàn) times the previous. |
3 | 10^{8} | 10^{16} | 10^{24} | 10^{32} | 10^{40} | 10^{48} | Each numeral is 10^{8} (万万 wànwàn) times the previous. |
4 | 10^{8} | 10^{16} | 10^{32} | 10^{64} | 10^{128} | 10^{256} | 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 is generally consistent through Chinese communities, as well as in Japan. However, most people do not recognize numerals beyond 兆 (zhào) (10^{12}) and dictionary definitions on these larger number words may not be consistent.
SI prefixes
The definition of 兆 (zhào) = 10^{6} survived in a translation for the SI prefix mega, since there will be no single numeral for that value otherwise. That has caused much confusion.
Further complicating the matter, an early attempt to translate SI prefixes used larger, rarer numerals for larger multiples, such as 京 (jīng) for giga, and rarer fractional numerals for smaller fractions, such as 纖 (xiān) for nano, creating even more values for each numeral.
Today, both the governments of the People's Republic of China (Mainland China, Hong Kong and Macau) and Republic of China (Taiwan) have adopted standards that use phonetic transliterations for the prefixes. However, there are differences in the choices of characters, and the definition of 兆 (zhào) is different between the two standards. The following table lists the two different systems together with the early translation.
Value | Symbol | English | Early translation | PRC standard | ROC standard |
---|---|---|---|---|---|
10^{24} | Y | yotta | 尧 yáo | 佑 yòu | |
10^{21} | Z | zetta | 泽 zé | 皆 jiē | |
10^{18} | E | exa | 穰 ráng | 艾 ài | 艾 ài |
10^{15} | P | peta | 秭 zǐ | 拍 pāi | 拍 pāi |
10^{12} | T | tera | 垓 gāi | 太 tài | 兆 zhào |
10^{9} | G | giga | 京 jīng | 吉 jí | 吉 jí |
10^{6} | M | mega | 兆 zhào | 兆 zhào | 百萬 bǎiwàn |
10^{3} | k | kilo | 千 qiān | 千 qiān | 千 qiān |
10^{2} | h | hecta | 百 bǎi | 百 bǎi | 百 bǎi |
10^{1} | 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 huama (花碼) numerals
Just like Ancient Englishman used the Roman numerals for doing mathematics or commerce, Ancient Chinese used the rod numerals which is a positional system. The "Hua1 Ma3" 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 "Hua1 Ma3" system are represented in a similar way as on the abacus.
Nowadays, the huama 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.
The misnomer remains in the Unicode standard.
In the huama 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 |
The top row contains the numeric symbols, for example, 〤〇〢二 stands for 4022. The bottom row consists of one or more Chinese characters that represents the unit of the first digit in the first row. The first part in the bottom row indicates the order of the first digit in the top row, e.g. qian1 (千) for thousand, bai3 (百) for hundred, shi2 (拾) for ten, blank for one etc. The second part denotes the unit of measurement, such as yuán (元 U+5143 for dollar) or mao2 (毫 U+4EB3 or 毛 U+6BDB for 10 cents) or xiān (仙 U+4ED9 for 1 cent) or lǐ (里 U+91CC for Chinese mile) or any other measurement unit. If the characters 'shí yuán' (拾元 or 10 dollars) are below the digits XO||=, it is then read as forty dollars and twenty two cents. Notice that the decimal point is implicit when the first digit '4' is set at the 'ten' position. This is very similar to the modern scientific notation for floating point numbers where the significant digits are represented in the mantissa and the order of magnitude is specified in the exponent.
When written vertically, the above example is written thus:
〤〇〢二 拾 元 |
The digits of the Suzhou numerals are defined between U+3021 and U+3029 in Unicode.
Zero is represented by a circle, probably numeral '0', letter 'O' or character U+3007 may work well. Leading and trailing zeros are unnecessary in this system. Additional characters representing 10, 20, 30 and 40 are encoded as U+5341 (十), U+5344 (卄), U+5345 (卅), U+534C (卌) respectively.
For those who cannot see the Unicode glyphs in the web browser, here are the descriptions of the appearance of these digits:
- 0 is a circle (exact Unicode unknown, perhaps 〇 U+3007)
- 1 is one horizontal (一 U+4E00) or vertical (〡 U+3021) stroke
- 2 is two horizontal (二 U+4E8C) or vertical (〢 U+3022) strokes
- 3 is three horizontal (三 U+4E09) or vertical (〣 U+3023) strokes
- 4 is a cross that looks like X (〤 U+3024)
- 5 is a loop (〥 U+3025)
- 6 is a dot (signify 5 the same way as on an abacus) on top of one horizontal stroke (〦 U+3026)
- 7 is a dot on top of two horizontal strokes (〧 U+3027)
- 8 is a dot on top of three horizontal strokes (〨 U+3028)
- 9 is a dot on top of a variant of the 〤 (4) symbol (〩 U+3029); this symbol looks like the Chinese character for "jiu3 (久 U+4E45)", compare to the formal character '9' "jiu3 (玖 U+7396)". (Some web browsers, e.g. IE 5.5, display this character incorrectly as the "fan3 wen2", or reverse "wen2" 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 ||— instead of || | which can be confused with 3.
Hand gestures
Main article at: Chinese number gestures.
There is a common method of using of one hand to signify the numbers one through ten. While the five digits on one hand can express the numbers one through five, six through 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. 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.
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