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Chinese numerals are words and characters used to denote in .

Today, speakers of Chinese languages use three written : the system of used worldwide, and two indigenous systems. The more familiar indigenous system is based on Chinese characters that correspond to numerals in the spoken language. These may be shared with other languages of the Chinese cultural sphere such as , Japanese, and Vietnamese. Most people and institutions in China primarily use the Arabic or mixed Arabic-Chinese systems for convenience, with traditional Chinese numerals used in finance, mainly for writing amounts on cheques, banknotes, some ceremonial occasions, some boxes, and on commercials.

The other indigenous system consists of the , or huama, a positional system, the only surviving form of the . These were once used by Chinese mathematicians, and later by merchants in Chinese markets, such as those in until the 1990s, but were gradually supplanted by Arabic numerals.


Basic counting in Chinese
The Chinese character numeral system consists of the Chinese characters used by the Chinese written language to write spoken numerals. Similar to spelling-out numbers in English (e.g., "one thousand nine hundred forty-five"), it is not an independent system per se. Since it reflects spoken language, it does not use the positional system as in , in the same way that spelling out numbers in English does not.


Ordinary numerals
There are characters representing the numbers zero through nine, and other characters representing larger numbers such as tens, hundreds, thousands, ten thousands and hundred millions. There are two sets of characters for Chinese numerals: one for everyday writing, known as (), and one for use in commercial, accounting or financial contexts, known as ( or 'capital numbers'). The latter were developed by () and were further refined by the (). They 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. 大寫數字「 A forger could easily change the everyday characters (30) to (5000) just by adding a few strokes. That would not be possible when writing using the financial characters (30) and (5000). They are also referred to as "banker's numerals" or "anti-fraud numerals". For the same reason, rod numerals were never used in commercial records.

0or Usually is preferred, but in some areas, 〇 may be a more common informal way to represent zero. The original Chinese character is or , is referred as remainder something less than 1 yet not nil referred. The traditional is more often used in schools. In Unicode, 〇 is treated as a Chinese symbol or punctuation, rather than a Chinese ideograph.
1 Also (obsolete financial), can be easily manipulated into or .
2 Also (obsolete, financial), can be easily manipulated into or . Also .
3 Also (obsolete financial), which can be easily manipulated into or .
4 Also (obsolete financial).
5
6
7
8
9
10 Although some people use as financial, it is not ideal because it can be easily manipulated into or .
100
1,000
104 Chinese numbers group by ten-thousands; see Reading and transcribing numbers below.
108 For variant meanings and words for higher values, see Large numbers below.
1. Wugniu is a pan-Wu romanization scheme, but the exact romanization depends on the variety. The romanization listed here is specifically for Shanghainese.


Regional usage
0 Historically, the use of 空 for 'zero' predates 零. This is now archaic in most varieties of Chinese, but it is still used in most of .
0 Literally 'a hole', is analogous to the shape of and , it is used to unambiguously pronounce #0 in radio communication.
1 Literally 'the smallest', it is used to unambiguously pronounce #1 in radio communication. This usage is not observed in Cantonese except for , which refers to a special winning hand in .
1 In most , there are two words meaning 'one'. For example, in , is used before a classifier: 'one person' is , not . In , is often used for both and , but some authors differentiate, writing for and for .
2 Used instead of before a classifier. For example, 'two people' is , not . However, in some lects such as Shanghainese, is the generic term used for two in most contexts, such as and not . It appears where 'a pair of' might in English, but is always used in such cases. It is also used for numbers, with usage varying from dialect to dialect, even person to person. For example, '2222' can be read as , , or even in Mandarin. It is used to unambiguously pronounce #2 in radio communication.
2 In regional dialects of Northeastern Mandarin, represents a "lazy" pronunciation of within the local dialect. It can be used as an alternative for , e.g. , as opposed to . A measure word never follows .
3 In regional dialects of Northeastern Mandarin, represents a "lazy" pronunciation of three within the local dialect. It can be used as a general number to represent 'three', e.g.; , or as an alternative for , e.g. , as opposed to ). Regardless of usage, a measure word never follows .
7 Literally 'a turn' or 'a walking stick' and is analogous to the shape of and , it is used to unambiguously pronounce #7 in radio communication.
9 Literally 'a hook' and is analogous to the shape of , it is used to unambiguously pronounce #9 in radio communication.
10 In spoken , can be used in place of when it is used in the middle of a number, preceded by a multiplier and followed by a ones digit, e.g. '63', it is not used by itself to mean 10. This usage is not observed in Mandarin.
廿20 A contraction of . 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. In spoken , can be used in place of when followed by another digit such as in numbers 21–29 (e.g. '23', a measure word, e.g. , a noun, or in a phrase like 'twenty-something'. It is not used by itself to mean 20. is still used in place of in Southern Min and Wu. 卄 is a rare variant.
30 A contraction of . The written form is still used to abbreviate date references in Chinese. For example, May 30 Movement (). The spoken form is still used in various dialects of Chinese. In spoken , can be used in place of when followed by another digit such as in numbers 31–39, a measure word (e.g. ), a noun, or in phrases like 'thirty-something'. It is not used by itself to mean 30. When spoken is pronounced as . Thus '31', is pronounced as .
40 A contraction of . Found in historical writings written in . Spoken form is still used in various dialects of Chinese, albeit very rare. See Reading and transcribing numbers section below. In spoken Cantonese can be used in place of when followed by another digit such as in numbers 41–49, a measure word (e.g. ), a noun, or in phrases like 'forty-something', it is not used by itself to mean 40. When spoken, is pronounced as . Thus , is pronounced as . Similarly, in Southern Min 41 can be referred to as .
200 Very rarely used; one example is in the name of a library in , .


Powers of 10

Large numbers
For numbers larger than 10,000, similarly to the long and short scales in the West, there have been four systems in ancient and modern usage. The original one, with unique names for all powers of ten up to the 14th, is ascribed to the in the 6th century book by Zhen Luan, . In modern Chinese, only the second system is used, in which the same ancient names are used, but each represents a , times the previous:
In practice, this situation does not lead to ambiguity, with the exception of , which means 1012 according to the system in common usage throughout the Chinese communities as well as in Japan and , but has also been used for 106 in recent years (especially in mainland China for ). To avoid problems arising from the ambiguity, the PRC government never uses this character in official documents, but uses ) or instead. Partly due to this, combinations of and are often used instead of the larger units of the traditional system as well, for example instead of . The ROC government in uses to mean 1012 in official documents.


Large numbers from Buddhism
Numerals beyond zǎi come from in , but are mostly found in ancient texts. Some of the following words are still being used today, but may have transferred meanings.

ke̍k 1048Literally 'extreme'.
hîng-hô-sua 1052Literally 'sands of the ', a metaphor used in a number of referring to many individual grains of sand
a-sing-kîa1-sen-ji1056From Sanskrit असंख्येय 'innumerable', 'infinite'
ná-iû-thann 1060From Sanskrit नियुत 'myriad'
put-khó-su-gī 1064Literally translated as "unfathomable". This word is commonly used in Chinese as a , meaning "unimaginable", instead of its original meaning of the number 1064.
bû-liōng tāi-siàu 1068literally 'without measure', and can mean 1068. This word is also commonly used in Chinese as a commendatory term, means 'no upper limit'. e.g.: 'a great future'. 'a large number', and can mean 1072.


Small numbers
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 have fallen into disuse.

10−12(Ancient Chinese)
corresponds to the SI prefix [[pico-]].
     
miǎo10−11(Ancient Chinese)
āi10−10(Ancient Chinese)
chén10−9Literally 'dust'
(S) corresponds to the SI prefix [[nano-]].
     
shā10−8Literally, "Sand"
xiān10−7'fiber'
wēi10−6still used, corresponds to the SI prefix .
10−5(Ancient Chinese)
10−4also . Literally, "Thread"
háo10−3also . still in use, corresponds to the SI prefix .
also . still in use, corresponds to the SI prefix .
fēn10−1still in use, corresponds to the SI prefix .


Small numbers from Buddhism
10−24'Nirvana's tranquillity'
corresponds to the SI prefix [[yocto-]].
     
10−23From Sanskrit अमल
10−22From Sanskrit आलय
10−21'quiet'
corresponds to the SI prefix [[zepto-]].
     
10−20'void'
10−19Literally 'six virtues'
10−18Literally 'brevity', from Sanskrit क्षण . corresponds to the SI prefix .
10−17Literally 'flick of a finger'. Still commonly used in the phrase
10−16Literally 'moment of breath'. Still commonly used in the 'many things changed in a very short time'
10−15Rarely used in modern Chinese as 'a very short time'. corresponds to the SI prefix .
10−14
10−13'blurred'


SI prefixes
In the People's Republic of China, the early translation for the in 1981 was different from those used today. The larger (, , , , ) and smaller Chinese numerals (, , , , ) were defined as translation for the SI prefixes as mega, giga, tera, peta, exa, micro, nano, pico, femto, atto, resulting in the creation of yet more values for each numeral. 1981 Gazette of the State Council of the People's Republic of China , No. 365 , page 575, Table 7: SI prefixes

The Republic of China (Taiwan) defined as the translation for mega and as the translation for tera. This translation is widely used in official documents, academic communities, informational industries, etc. However, the civil broadcasting industries sometimes use to represent "".

Today, the governments of both China and 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.

+ SI Prefixes
  kūn kūn
  róng luó
  yáo yòu
  jiē
ài ài
pāi pāi
tài zhào
zhào bǎiwàn
qiān qiān
bǎi
shí shí
 
fēn fēn
háo háo
wēi wēi wēi
xiān nài
fēi fēi
miǎo à à
  jiè
  yāo yōu
  róu róng
  kuī kuì


Reading and transcribing numbers

Whole 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, the multiplier labels=no ( liǎng) is often used rather than for all numbers 200 and greater with the "2" numeral (although as noted earlier this varies from dialect to dialect and person to person). Use of both or are acceptable for the number 200. When writing in the Cantonese dialect, is used to represent the "2" numeral for all numbers. In the dialect of Chaozhou (), ( no6) is used to represent the "2" numeral in all numbers from 200 onwards. Thus:

For the numbers 11 through 19, the leading 'one' (labels=no) 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:

or

Notes:

  1. Nothing is ever omitted in large and more complicated 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 ().

Outside of Taiwan, digits are sometimes grouped by instead of 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 × = . 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):

In Taiwan, pure Arabic numerals are officially always and only grouped by thousands. Unofficially, they are often not grouped, particularly for numbers below 100,000. Mixed Arabic-Chinese numerals are often used in order to denote myriads. This is used both officially and unofficially, and come in a variety of styles:

1,234萬5千
123,450,000(1) 1,0000,0000 (2345) 1,0000
12,345(1) 1,0000 (2345)

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:

or


Fractional values
To construct a fraction, the is written first, followed by , then the literary possessive particle , and lastly the . 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. For example, to express "two thirds", the structure "three parts of-this two" is used. are written with the whole-number part first, followed by , then the fractional part.

Percentages are constructed similarly, using as the denominator. (The number 100 is typically expressed as , like the English 'one hundred'. However, for percentages, is used on its own.)

25%
110%

Because percentages and other fractions are formulated the same, Chinese are more likely than not to express 10%, 20% etc. as 'parts of 10' (or , , etc. i.e. 十分之一; , 十分之二; , etc.) rather than "parts of 100" (or , , etc. i.e. 百分之十; , 百分之二十; , etc.)

In Taiwan, the most common formation of percentages in the spoken language is the number per hundred followed by the word , a contraction of the Japanese パーセント; , itself taken from 'percent'. Thus 25% is 二十五趴; .

Decimal numbers are constructed by first writing the whole number part, then inserting a point (), and finally the fractional part. The fractional part is expressed using only the numbers for 0 to 9, similarly to English.

16.98
12345.6789
75.4025
0.1

functions as a number and therefore requires a measure word. For example: .
     


Ordinal numbers
Ordinal numbers are formed by adding before the number.
1st
2nd
82nd
The are a traditional Chinese ordinal system.


Negative numbers
Negative numbers are formed by adding before the number.
−1158
−75.4025


Usage
requires the use of classifiers (measure words) when a numeral is used together with a noun to express a quantity. For example, "three people" is expressed as p=sān ge rén, "three (labels=no particle) person", where labels=no/p= labels=no is a classifier. There exist many different classifiers, for use with different sets of nouns, although labels=no/p= is the most common, and may be used informally in place of other classifiers.

Chinese uses in certain situations in which English would use . For example, labels=no (literally "three ") means "third floor" ("second floor" in British ). Likewise, c=二十一世纪/二十一世紀 (literally "twenty-one century") is used for "21st century".Yip, Po-Ching; Rimmington, Don, Chinese: A Comprehensive Grammar, Routledge, 2004, p. 12.

Numbers of years are commonly spoken as a sequence of digits, as in t= ("two zero zero one") for the year 2001.Yip, Po-Ching; Rimmington, Don, Chinese: A Comprehensive Grammar, Routledge, 2004, p. 13. Names of months and days (in the Western system) are also expressed using numbers: t= ("one month") for January, etc.; and t= ("week one") for Monday, etc. There is only one exception: Sunday is t=, or informally t=, both literally "week day". When meaning "week", "t=" p=xīngqī and "first=t" c= are interchangeable. "t=" c= or "t=" c= means "day of worship". Chinese Catholics call Sunday "t=" c=, "Lord's day".

Full dates are usually written in the format 2001年1月20日 for January 20, 2001 (using t= "year", t= "month", and t= "day") – all the numbers are read as cardinals, not ordinals, with no leading zeroes, and the year is read as a sequence of digits. For brevity the c=, c= and c= may be dropped to give a date composed of just numbers. For example "6-4" in Chinese is "six-four", short for "month six, day four" i.e. June Fourth, a common Chinese shorthand for the 1989 Tiananmen Square protests (because of the violence that occurred on June 4). For another example 67, in Chinese is sixty seven, short for year nineteen sixty seven, a common Chinese shorthand for the Hong Kong 1967 leftist riots.


Counting rod and Suzhou numerals
In the same way that were standard in ancient and medieval Europe for mathematics and commerce, the Chinese formerly used the , which is a positional system. The Suzhou numerals (p=Sūzhōu huāmǎ) system is a variation of the rod numerals. Nowadays, the huāmǎ system is only used for displaying prices in Chinese markets or on traditional handwritten invoices.


Hand gestures
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 easily express the numbers one to five, six to ten have special signs that can be used in commerce or day-to-day communication.


Historical use of numerals in China
Most Chinese numerals of later periods were descendants of the oracle numerals of the 14th century BC. The oracle bone script numerals were found on tortoise shell and animal bones. In early civilizations, the Shang were able to express any numbers, however large, with only nine symbols and a counting board though it was still not positional.The Shorter Science & Civilisation in China Vol 2, An abridgement by Colin Ronan of Joseph Needham's original text, p5, Cambridge University Press

Some of the bronze script numerals such as 1, 2, 3, 4, 10, 11, 12, and 13 became part of the system of .

In this system, horizontal rod numbers are used for the tens, thousands, hundred thousands etc. It is written in that "one is vertical, ten is horizontal". Chinese Wikisource 孫子算經: , , , , .

71824

The counting rod numerals system has place value and decimal numerals for computation, and was used widely by Chinese merchants, mathematicians and astronomers from the to the 16th century.

Alexander Wylie, Christian missionary to China, in 1853 already refuted the notion that "the Chinese numbers were written in words at length", and stated that in ancient China, calculation was carried out by means of counting rods, and "the written character is evidently a rude presentation of these". After being introduced to the rod numerals, he said "Having thus obtained a simple but effective system of figures, we find the Chinese in actual use of a method of notation depending on the theory of local value i.e., several centuries before such theory was understood in Europe, and while yet the science of numbers had scarcely dawned among the Arabs."Alexander Wylie, Jottings on the Sciences of the Chinese, North Chinese Herald, 1853, Shanghai

During the and dynasties (after Arabic numerals were introduced into China), some Chinese mathematicians used Chinese numeral characters as positional system digits. After the Qing period, both the Chinese numeral characters and the Suzhou numerals were replaced by Arabic numerals in mathematical writings.


Cultural influences
Traditional Chinese numeric characters are also used in and and were used in before the 20th century. 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.


See also


Notes
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