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Chinese numerals

Numeral systems

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Numeral system

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Today, speakers of Chinese use three numeral systems: There is the ubiquitous system of Arabic digits and two ancient Chinese numeral systems. The "Hua1 Ma3 (花碼 U+82B1, U+78BC for "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 "Hua1 Ma3" 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 'Hua1'.

Table of contents
1 Written numbers
2 Suzhou (蘇州) or Hua Ma (花碼) numerals
3 See also
4 External links

Written numbers

The Chinese character numeral system is not a positional system. Instead, it is based on decimal bundling. The rules for forming numbers are as follows:

  1. The numeral characters are tightly integrated into the language: Each numeral character has a phonetic value and a number is read by pronouncing each individual character it consists of, unlike e.g. English, where the numeral '2' has to be pronounced 'two' or 'twenty' depending on position.

  2. There are ten 'basic' numeral characters representing the numbers zero through nine. And there are other characters representing big numbers such as tens, hundreds, thousands etc. There are two sets of characters for Chinese numerals, one in formal writing and one in casual daily use writing. The formal version is much more complex to prevent alteration in legal documents such as promissory notes.


    Their phonetic values in     Mandarin are:

    Pinyin Formal writing Casual writing Value Notes
    ling2 零 〇 zero Casual form is a circle (U+3007, Ideographic number zero)
    yi1 壹 一 one 么 (yao1), "the smallest", is used widely in the People's Republic of China (including Hong Kong and Macau) as a Synonym>synonym of "one", but never so in the Republic of China on Taiwan, except for soldiers.
    er4 貳 二 two 兩 (simplified 两) (liang3) is often used when placed before a quantifier (see Measure word>measure word)
    san1 叄 三 three 弎 (obsolete)
    參 is also acceptable.
    si4 肆 四 four  
    wu3 伍 五 five  
    liu4 陸 六 six  
    qi1 柒 七 seven  
    ba1 捌 八 eight  
    jiu3 玖 九 nine  
     
    shi2 拾 十 ten  
    bai3 佰 百 hundred  
    qian1 仟 千 thousand  
    wan4 萬 万 104 or myriad Western numbers group by thousands, Chinese numbers group by wan4.
     
    yi4 億 亿 108 (hundred million) It also means 10 wan4 (1_E5>105) in some ancient context.

    See explanation below for inconsistency of values for numerals greater than wan4.
    zhao4 兆   1012 (trillion) 109) in American numbers.
    It also means 100 wan4 (106) when used as an SI prefix to SI units in Mainland China, Hong Kong and Macau, e.g. zhao4he4 兆赫 = Megahertz (MHz). In Taiwan, it is called bai3wan4he4 百萬赫.
    In some ancient context, 1 zhao4 = 1 yi4 yi4 (1016).
    jing1 京
    (or 經)     		  1016 107 or 1032.
    gai1 垓   1020 108 or 1064.
    zi3 秭   1024 109 or 10128.
    rang2 穰   1028 (Ancient Chinese) It may also mean 1010 or 10256.
    gou1 溝   1032 (Ancient Chinese) It may also mean 1011 or 10512.
    jian4 澗   1036 1012 or 101024.
    zheng4 正   1040 (Ancient Chinese) It may also mean 1013 or 102048.
    zai4 載   1044 (Ancient Chinese) It may also mean 1014 or 104096.
    ji2 極   1048 (Ancient Chinese) It may also mean1 1015 or 108192.
     
    fen1 分   tenth, deci-  
    li2 釐 厘 centi-  
    hao2 毫   milli-  
    si1 絲   10-4 (ten-thousandth) (Uncommon Usage)
    hu1 忽   10-5 (hundred-thousandth) (Uncommon Usage)
    wei1 微   -6 (millionth, Micro>micro-)  
    xian1 纖   10-7 (Ancient Chinese)
    sha1 沙   10-8 (Ancient Chinese)
    chen2 塵   10-9 (Ancient Chinese)
    ai1 埃   10-10 (Ancient Chinese)
    miao3 渺   10-11 (Ancient Chinese)
    mo4 漠   10-12 (Ancient Chinese)

  3. Leading '1' can sometimes be abbreviated when it is understood. The numbers 11 - 19 are often written using two characters, where the first one is the basic numeral '10' and the second one is one of the basic numerals '1' to '9'. (i.e. 14 is written as '10' '4' as an abbreviation from '1' '10' '4'.) The leading '1' in other positions can be abbreviated only in conversation (common in Cantonese). For example, 17000 can be read as '10000' '7', but written as '1' '10000' '7' '1000'. However, when more than two digits are involved, the abbreviation usually does not take place except in Japanese. For example, 114 is read as '1' '100' '1' '10' '4', and definitely not '100' '10' '4'. Although '1' '100' '10' '4' is marginally acceptable, it is not common.

  4. The numbers 20, 30, 40 ... 90 are constructed using a multiplicative principle, where, e.g., 60 is represented as '6' '10'; the numbers in between are formed like 11-19, so that, e.g., 42 is written as '4' '10' '2'. However, on calendars, there is a special character (廿) used for "twenty" in the numbers 21 through 29. (Twenty itself is written '2' '10'.)

  5. There are also numeral characters for hundred (bai3), thousand (qian1), myriad (wan4) and hundred million (yi4) and trillion (zhao4). The above principles are extended, except a new grouping character is introduced for each myriad (wan4) times of the previous number. For example, one yi4 = 10000 wan4; one zhao4 = 10000 yi4. Hence it is more convenient to read if the digits are separated four in a group. For example, 12,345,678,901,203 is regrouped as 12,3456,7890,1203 to read or write as

    shi2 er4 zhao4 san1 qian1 si4 bai3 wu3 shi2 liu4 yi4 qi7 qian1 ba1 bai3 jiu3 shi2 wan4 yi1 qian1 er4 bai3 ling2 san1.
    (十二兆三千四百五十六億七千八百九十萬一千二百零三)

    which is equivalent to say

    (*) ten 2 trillion 3 thousand 4 hundred 5 ten 6 byriad 7 thousand 8 hundred 9 ten (*) myriad 1 thousand 2 hundred 0 3.

    (*) denotes where a character is understood and omitted.

    This may seem very complicated, but it actually is very similar to reading an English number. The only differences are that myriad is used as a grouping unit instead of the usual thousand, and ten is written explicitly instead of appending the suffix ty or teen to the number.

    Compare to a grouping of three digits in the English system, 12,345,678,901,203 is read as

    12 trillion 3 hundred 4ty 5 billion 6 hundred 7ty 8 million 9 hundred 'and' 1 thousand 2 hundred 'oh' 3.

  6. 'Interior zeroes' before the unit position (as in 10002) have to be spelt explicitly, so 10002 becomes '1' '10000' '0' '2'; the reason for this is that '1' '10000' '2' is used as a shorthand for '1' '10000' '2' '1000' where the trailing '1000' is abbreviated. One '0' is sufficient to resolve the ambiguity. Same rule applies to the unit position before each grouping character. For example, 10050000 is read '1' '1000' '0' '5' '10000'. However, 1032 can be read as '1' '1000' '0' '3' '10' '2'. In this case, the '0' is preferred but optional because the '3' '10' '2' is not ambiguous -- oh, and try to avoid the use of '2' '100' '5' (er bai wu i.e. 250) in conversational language; it is normally used to mean stupid. Note that 205 is read with the explicit interior zero, i.e. '2' '100' '0' '5' (er bai ling wu).

  7. For numeral characters greater than wan4, actually there were three systems in ancient records:
    System yi4 zhao4 jing1 gai1 zi3 rang2 Notes
    1 105 106 107 108 109 1010 Each numeral increases by the factor of shi2 (10).
    2 108 1012 1016 1020 1024 1028 Each numeral increases by the factor of wan4 (10000).
    3 108 1016 1032 1064 10128 10256 Each numeral increases by the factor of the preceding one.
    Modern Chinese and Japanese use only the second system. The usage is consistent throughout all Chinese communities. However, most people do not recognize numerals beyound zhao4 (1012) and their definitions on dictionaries may not be consistent. The definition of zhao4 = 106 survived in the translation for the SI prefix Mega, since there will be no single numeral for that value otherwise. There was also an attempt to use the rarely used numerals jing1, gai1, zi3, rang2... to translate SI prefixes giga (109), tera (1012), peta (1015), exa (1018)... making the situation even more complicated. Fortunately the current national standard of the People's Republic of China uses phonetic transcriptions ji2 吉, tai4 太, pai1 拍, ai4 艾... instead.

Strictly speaking, the Chinese written numbers should not be considered a numeral system. As an analogy, when the value 3000 is written as two English words "Three Thousand", the English words are not part of the number system. (or are they?)

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 "Hual 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 "Hual Ma3" system are represented in a similar way as on the abacus.

Suzhou (蘇州) or Hua Ma (花碼) numerals

Nowadays, the "Hua1 Ma3" 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 "Hua1 Ma3" system, special symbols are used for digits instead of the Chinese characters. The digits are positional. 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, XO||= (〤〇〢二) or XO=|| stands for 4022. The bottom row consists of one or more Chinese characters. The first 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 character denotes the unit, such as yuan2 (元 U+5143 for dollar) or mao2 (毛 U+6BDB for 10 cents) or sian1 (仙 U+4ED9 for 1 cent) or li2 (里 U+91CC for Chinese mile) or any measurement unit. If the characters 'shi2 yuan2' (拾元 or 10 dollars) are below the digits XO||=, it is then read as forty dollar and twenty two cents. Notice 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.

The "Hua1 Ma3" system in Hong Kong is definitely using the same Suzhou numerals symbols. However, it is unsure if the stacked arrangement is also the same in the Suzhou system. Wikis from other parts of China please confirm if the "Hua1 Ma3" system is the same as Suzhou system.

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 and 30 are encoded as U+3038, U+3039, U+303A, respectively.

For those who cannot see the Unicode glyphs in the web browser, here are the descriptions of the appearance of these digits:

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.

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 recognized and used in Japan where they are used in much the same formal or decorative fashion that Roman Numerals are in Western cultures. In Japan, Chinese numerals often appear on the same signs or documents as the more commonly used Western style numbers.

See also

External links