Chinese numerals

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 and the character writing system become, however, gradually supplanted by the Arabic system. 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 number in long form such as on checks.

Individual Chinese characters mentioned in this article can be looked up graphically in the Unihan database (http://www.unicode.org/charts/unihan) 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' (http://www.unicode.org/cgi-bin/GetUnihanData.pl?codepoint=82B1).

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 U+96F6	〇 U+3007	zero	U+3007 is a circle
   yi1	壹 U+58F9	一 U+4E00	one	弌 U+5F0C (obsolete). 么 (yao1), "the smallest", is used widely in China (including Hong Kong and Macau) as a synonym of "one", but never so in Taiwan, except for soldiers.
   er4	貳 U+8CB3	二 U+4E8C	two	弍 U+5F0D (obsolete)
   san1	叄 U+53C4	三 U+4E09	three	參 U+53C3 is also acceptable; 弎 U+5F0E (obsolete)
   si4	肆 U+8086	四 U+56DB	four
   wu3	伍 U+4F0D	五 U+4E94	five
   liu4	陸 U+9678	六 U+516D	six
   qi1	柒 U+67D2	七 U+4E03	seven
   ba1	捌 U+634C	八 U+516B	eight
   jiu3	玖 U+7396	九 U+4E5D	nine
   shi2	拾 U+62FE	十 U+5341	ten
   bai3	佰 U+4F70	百 U+767E	hundred[?]
   qian1	仟 U+4EDF	千 U+5343	thousand[?]
   wan4	萬 U+842C	万 U+4E07	104[?] or myriad
   jing1	京 U+4EAC		108[?] (ten million)	Ancient Chinese
   yi4	億 U+5104	亿 U+4EBF	108[?] (hundred million)
   gai1	垓 U+5793		108[?] (hundred million)	Ancient Chinese
   zi3	秭 U+79ED		109[?] (billion).	Ancient Chinese
   zhao4	兆 U+5146	兆 U+5146	1012[?] (trillion).
   fen1	分 U+5206		tenth
   hao2	毫 U+6BEB		hundredth
   li2	釐 U+91D0		thousandth

   (*) Notice that the digits are separated in group of 4 here because it is the way Chinese numbers are read. More will be explained below.

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).

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.

Hangzhou (杭州) 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 "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 Hangzhou numerals symbols. However, it is unsure if the stacked arrangement is also the same in the Hangzhou system. Wikis from other parts of China please confirm if the "Hua1 Ma3" system is the same as Hangzhou system.

The digits of the Hangzhou 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:

• 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 look 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 symbol (〩 U+3029) 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, click here (http://www.unicode.org/cgi-bin/GetUnihanData.pl?codepoint=3029) 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 others. 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 Hangzhou 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: Numeral system, Arabic numerals, Armenian numerals, Babylonian numerals, Greek numerals, Hebrew numerals, Indian numerals, Mayan numerals, Roman numerals, and Chinese characters.

External links

• Unicode reference glyphs showing the Hangzhou numerals (http://www.unicode.org/charts/PDF/U3000.pdf)