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March 8, 2014 |
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Today, speakers of Chinese language|Chinese use three numeral systems: the ubiquitous system of Arabic numerals|Arabic digits, along with two ancient Chinese numeral systems. The huama (zh-d-cp|p=huāmǎ|c=花碼; 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 numerals|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 http://www.unicode.org/charts/unihan.html 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 http://www.unicode.org/cgi-bin/GetUnihanData.pl?codepoint=82B1 'huā'. 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 ten characters representing the numbers zero through nine, and other characters representing big numbers such as tens, hundreds, thousands etc. There are two sets of characters for Chinese numerals, one in everyday writing and one restricted to 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.
<li>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 language|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. (Though not generally acceptable in modern use, in certain older texts (a prime example being the Protestant Bible) or in poetic usages, 114 may be written as '100' '10' '4'.) <li>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 or 卄 pinyin nian4) used for "twenty" in the numbers 21 through 29. (Twenty itself is written '2' '10'.) There are special characters (卅 pinin sa4 and 卌 pinyin xi4) used for "thirty" and "forty" respectively in the same manner. <li>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. <br>(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. <li>'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). <li>For numeral characters greater than wan4, actually there were four systems in ancient and modern usage:
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 (10<sup>12</sup>) and their definitions on dictionaries may not be consistent. The definition of zhao4 = 10<sup>6</sup> 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_prefix|SI prefixes giga (10<sup>9</sup>), tera (10<sup>12</sup>), peta (10<sup>15</sup>), exa (10<sup>18</sup>)... 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. </ol> 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 "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 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: <table> <tr> <td> <td align=center> 〤〇〢二 <br> 拾元 </table> 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 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: <table> <tr> <td align=center> <td align=center> 〤〇〢二 <br> 拾<br>元 </table> 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:
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 dynasty|Ming and Qing dynasty|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.
de:Chinesische_Zahlen es:Numeraci?n china fi:Kiinalaiset numerot fr:Num?ration chinoise zh:中文数字 This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Chinese numerals".
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