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|Numeral systems by culture|
|Positional systems by base|
|Non-standard positional numeral systems|
|List of numeral systems|
The more familiar indigenous system are Chinese characters that correspond to numerals in the spoken language[disambiguation needed]. These are shared with other languages of the Chinese cultural sphere such as Japanese, Korean and Vietnamese. Most people and institutions in China primarily use the Indian (Arabic) system for convenience, with traditional Chinese numerals used in finance, mainly for writing amounts on checks and banknotes and some ceremonial occasions.
The other indigenous system is the Suzhou numerals, or huama, a positional system. It is the only surviving form of the rod numerals. They were once used by Chinese mathematicians, and later in Chinese markets, such as those in Hong Kong before the 1990s, but has been gradually supplanted by the Arabic numerals and also the Roman numerals.
Written numbers 
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 Arabic numerals, in the same way that spelling out numbers in English does not.
Characters used to represent numbers 
Standard numbers 
There are 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 known as dàxiě (simplified Chinese: 大写; traditional Chinese: 大寫). 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. A forger could easily change everyday characters 三十 (30) to 五千 (5000) by adding just a few strokes. That would not be possible when writing using the financial characters 參拾 (30) and 伍仟 (5000). They are also referred to as "banker's numerals", "anti-fraud numerals", or "banker's anti-fraud numerals." For the same reason, rod numerals were never used in commercial records.
T denotes Traditional Chinese characters, S denotes Simplified Chinese characters.
|零||〇||0||líng||〇 is a common informal way to represent zero, but the traditional 零 is more often used in schools. 〇 is not a standard Chinese character, because Chinese characters never contain ovals (only boxes). In Unicode, 〇 is treated as a Chinese symbol or punctuation, rather than a Chinese ideograph.|
|壹||一||1||yī||also 弌 (obsolete financial), can be easily manipulated into 弍 (two) or 弎 (three).|
|貳 (T) or
|二||2||èr||also 弍 (obsolete financial), can be easily manipulated into 弌 (one) or 弎 (three).
also 兩 (T) or 两 (S), see Characters with regional usage section.
|參 (T) or
|三||3||sān||also 弎 (obsolete financial), can be easily manipulated into 弌 (one) or 弍 (two).
also 參(T) or 参(S) sān. Vulgar variants include 叄, 叁.
|肆||四||4||sì||also 䦉 (obsolete financial)|
|陸 (T) or
|拾||十||10||shí||Although some people use 什 as financial, it is not ideal because it can be easily manipulated into 伍 (five) or 仟 (thousand).|
|萬||萬 (T) or
|104||wàn||Chinese numbers group by ten-thousands
see Reading and transcribing numbers section below.
|億||億 (T) or
|108||yì||See large numbers section below.|
Characters with regional usage 
|Financial||Normal||Value||Pinyin (Mandarin)||Standard alternative||Notes|
|幺||1||yāo||一||Literally means "the smallest". It is used in Mandarin to unambiguously pronounce "#1" in series of digits (such as phone numbers and ID numbers), because one (一) rhymes with seven (七). It is never used in counting or reading values. In Taiwan, it is only used by soldiers, police, and emergency services. This usage is not observed in Cantonese except for 十三幺 (a special winning hand) in Mahjong.|
|2||liǎng||二||A very common alternative way of saying "two". Its usage varies from dialect to dialect, even person to person. For example "2222" can read as "二千二百二十二", "兩千二百二十二" or even "兩千兩百二十二" in Mandarin. See Reading and transcribing numbers section below.|
|呀||10||yā||十||In Cantonese speech, when 十 is used in the middle of a number, preceded by a multiplier and followed by a ones digit, 十 becomes 呀 (aa6), e.g. 六呀三, 63. This usage is not observed in Mandarin.|
|念||廿||20||niàn||二十||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 Cantonese, 廿 (jaa6) must be followed by another digit 1-9 (e.g. 廿三, 23), or in a phrase like 廿幾 ("twenty-something"); it is not used by itself to mean 20.
卄 is a rare variant.
|卅||30||sà||三十||The written form is still used to abbreviate date references in Chinese. For example, May 30 Movement (五卅運動).
Spoken form is still used in various dialects of Chinese. See Reading and transcribing numbers section below. As with 廿, 卅 must be used with another number to mean 卅幾 ("thirty-something") in Cantonese. Used in other dialects too, as well as historical writings.
|卌||40||xì||四十||Spoken form is still used in various dialects of Chinese, albeit very rare, as well as historical writings written in Classical Chinese.
As with 廿, 卌 must be used with another number to mean 卌幾 ("forty-something") in Cantonese. The usage of the word 卌 is done in the following matter, "sei(四) ah ##", or "4 ah ##". Thus 41 would be pronounced "sei ah yat", i.e. "four ah one".
|皕||200||bì||二百||Very rarely used, one common example is the literature 《皕宋樓》.|
Characters with military usage 
In the PLA, some numbers will have altered names when used for clearer radio communications. They are:
- 0: renamed 洞 (dòng)
- 1: renamed 幺 (yāo)
- 2: renamed 两 (liǎng)
- 4: renamed 刀 (dāo)
- 7: renamed 拐 (guǎi)
- 9: renamed 勾 (gōu)
Large numbers 
Similar 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 Yellow Emperor in the 6th century book by Zhen Luan, Wujing suanshu (Arithmetic in Five Classics). In modern Chinese only the second system is used, in which the same ancient names are used but each number is 10,000 (myriad, 萬 wàn) times the previous:
|Character (T)||億||兆||京||垓||秭||穰||溝||澗||正||載||Factor of increase|
|1||105||106||107||108||109||1010||1011||1012||1013||1014||Each numeral is 10 (十 shí) times the previous.|
|2||108||1012||1016||1020||1024||1028||1032||1036||1040||1044||Each numeral is 10,000 (万 wàn) times the previous.|
|3||108||1016||1024||1032||1040||1048||1056||1064||1072||1080||Each numeral is 108 (万乘以万 wàn chéng yǐ wàn, 10000 times 10000) times the previous.|
|4||108||1016||1032||1064||10128||10256||10512||101024||102048||104096||Each numeral is the square of the previous.|
In practice, this situation does not lead to ambiguity, with the exception of 兆 (zhào), which means 1012 according to the second system in common usage throughout the Chinese communities as well as in Japan and Korea, but is also used for 106 in recent years (esp. in mainland China to represent the Megabyte). To avoid problems arising from the ambiguity, the PRC government never uses this character in official documents, but uses 万亿 (wànyì) instead. The ROC government in Taiwan uses 兆 (zhào) to mean 1012 in official documents.
Numbers from Buddhism 
|This article may be expanded with text translated from the corresponding article in the Chinese Wikipedia. (September 2010)|
|Character (T)||Character (S)||Pinyin||Value||Notes|
|極||极||jí||1048||Literally means "Extreme"|
|恆河沙||恒河沙||héng hé shā||1052||Literally means "Sands of the Ganges"; a metaphor used in a number of Buddhist texts referring to the grains of sand in the Ganges River.|
|阿僧祇||ā sēng qí||1056||From Sanskrit Asaṃkhyeya|
|那由他||nà yóu tā||1060||From Sanskrit Nayuta|
|不可思議||不可思议||bùkě sīyì||1064||Literally translated as "unfathomable".|
|無量||无量||wú liàng||1068||Literally translated as "without measure"|
|大數||大数||dà shù||1072||Literally translated as "a large number"|
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.
|Character(s) (T)||Character(s) (S)||Pinyin||Value||Notes|
|涅槃寂靜||涅槃寂静||niè pán jì jìng||10−24||Literally, "Nirvana's Tranquility"
|阿摩羅||阿摩罗||ā mó luó||10−23||(Ancient Chinese)|
|阿頼耶||阿赖耶||ā lài yē||10−22||(Ancient Chinese)|
|清靜||清净||qīng jìng||10−21||Literally, "Quiet"
|虛空||虚空||xū kōng||10−20||Literally, "Void"|
|六德||liù dé||10−19||(Ancient Chinese)|
|剎那||刹那||chà nà||10−18||Literally, "Brevity"
|彈指||弹指||tán zhǐ||10−17||Literally, "Flick of a finger"|
|瞬息||shùn xī||10−16||Literally, "Moment of Breath"|
|須臾||须臾||xū yú||10−15||(Ancient Chinese)
|逡巡||qūn xún||10−14||(Ancient Chinese)|
|模糊||mó hu||10−13||Literally, "Blurred"|
|微||wēi||10−6||still in use, corresponds to the SI prefix micro-.|
|分||fēn||10−1||still in use, corresponds to the SI prefix deci-.|
SI prefixes 
In the People's Republic of China, the translations for the SI prefixes in 1981 were different from those used today. The larger (兆, 京, 垓, 秭, 穰) and smaller Chinese numerals (微, 纖, 沙, 塵, 渺) were defined as translations for the SI prefixes as mega, giga, tera, peta, exa', micro, nano, pico, femto, atto, resulting in the creation of more values for each numeral.
By the time of "1981 translation", a dispute had arisen over the value of 兆 . The government of the PRC used a part of this translation, and defined 兆 zhào as the translation for the SI prefix mega- (106). (Perhaps the government was not aware of the common usage of 兆, and thus did not consider an alternative single Chinese character, such as 巨, to represent mega.) Because of this, the translation has caused much confusion.
In addition, Taiwanese defined 百萬 as the translation for mega. This translation is widely used in official documents, academic communities, informational industries, etc. However, the civil broadcasting industries sometimes use 兆赫 to represent "megahertz".
Today, both the governments of the People's Republic of China (Mainland China, Hong Kong and Macau) and Republic of China (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.
|Value||Symbol||English||Early translation||PRC standard||ROC standard|
|1024||Y||yotta-||尧 yáo||佑 yòu|
|1021||Z||zetta-||泽 zé||皆 jiē|
|1018||E||exa-||穰 ráng||艾 ài||艾 ài|
|1015||P||peta-||秭 zǐ||拍 pāi||拍 pāi|
|1012||T||tera-||垓 gāi||兆 zhào||兆 zhào|
|109||G||giga-||京 jīng||吉 jí||吉 jí|
|106||M||mega-||兆 zhào||百万 bǎiwàn||百萬 bǎiwàn|
|103||k||kilo-||千 qiān||千 qiān||千 qiān|
|102||h||hecto-||百 bǎi||百 bǎi||百 bǎi|
|101||da||deca-||十 shí||十 shí||十 shí|
|100||(None)||one||一 yī||一 yī|
|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|
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 兩 (liǎng) is often used rather than 二 (èr) for all numbers greater than 200 with the "2" numeral (although as noted earlier this varies from dialect to dialect and person to person). Use of both 兩 (liǎng) or 二 (èr) are acceptable for the number 200. When writing in the Cantonese dialect, 二 (yi6) is used to represent the "2" numeral for all numbers. In the southern Min dialect of Chaozhou (Teochew), 兩 (no6) is used to represent the "2" numeral in all numbers from 200 onwards. Thus:
|20||  or ||二十||二十 or 廿||二十||廿|
|200|| (èr) or (liǎng) ||二百 or 兩百||二百 or 兩百||兩百||兩百|
|2000|| (èr) or (liǎng) ||二千 or 兩千||二千 or 兩千||兩千||兩千|
|45||  ||四十五||四十五 or 卌五||四十五||四十五|
|2,362|| [1,000]     ||兩千三百六十二||二千三百六十二||兩千三百六十二||兩千三百六十二|
For the numbers 11 through 19, the leading "one" (一) 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:
|Number||Strict Putonghua||Colloquial or dialect usage|
|12000||   ||一萬兩千||  ||一萬二 or 萬二|
|114||    ||一百一十四||   ||一百十四|
|1158||      ||一千一百五十八||See note 1 below|
- Nothing is ever omitted in large and more complicated numbers such as this.
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 (萬) = yì (億). 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):
|(12) [1,0000,0000,0000] (3456) [1,0000,0000] (7890) [1,0000] (2345)||十二兆三千四百五十六億七千八百九十萬兩千三百四十五|
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:
|205||   ||二百〇五|
| [10,000]  ||十萬〇四|
|(1005) [10,000] (26) or
(1005) [10,000] (026)
Fractional values 
To construct a fraction, the denominator is written first, followed by 分之 ("parts of") and then the numerator. 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. Mixed numbers are written with the whole-number part first, followed by 又 ("and"), then the fractional part.
|2/3|| [parts of] ||三分之二|
|15/32||   [parts of]  ||三十二分之十五|
|1/3000||  [parts of] ||三千分之一|
|3 5/6|| [and]  [parts of] ||三又六分之五|
Percentages are constructed similarly, using 百 (100) as the denominator. The 一 (one) before 百 is omitted.
|25%|| [parts of]   ||百分之二十五|
|110%|| [parts of]    ||百分之一百一十|
Decimal numbers are constructed by first writing the whole number part, then inserting a point (simplified Chinese: 点; traditional Chinese: 點; pinyin: diǎn), and finally the decimal expression. The decimal expression is written using only the digits for 0 to 9, without multiplicative words.
|16.98||  [point]  ||十六點九八|
|12345.6789||         [point]    ||一萬兩千三百四十五點六七八九|
|75.4025||   [point]    ||七十五點四〇二五|
|0.1|| [point] ||〇點一|
Ordinal numbers 
Ordinal numbers are formed by adding 第 ("sequence") before the number.
|82nd||[sequence]   ||第八十二|
Negative numbers 
|-1158||[negative]       ||負一千一百五十八|
|-3 5/6||[negative]  [and]  [parts of] ||負三又六分之五|
|-75.4025||[negative]    [point]    ||負七十五點四〇二五|
Suzhou numerals 
In the same way that Roman numerals were standard in ancient and medieval Europe for mathematics and commerce, the Chinese formerly used the rod numerals, which is a positional system. The Suzhou numerals (simplified Chinese: 苏州花码; traditional Chinese: 蘇州花碼; pinyin: Sūzhōu huāmǎ) system is a variation of the Southern Song rod numerals. Nowadays, the huāmǎ system is only used for displaying prices in Chinese markets or on traditional handwritten invoices.
Counting rod numerals 
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 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 
Paleolithic numerals 
Neolithic numerals 
Shang oracle numerals 
Bronze script 
Some of the bronze script numerals such as 1, 2, 3, 4, 10, 11, 12, and 13 were passed to Rod numerals.
Rod numerals 
while horizontal rod numbers are used for the tens, thousands, hundred thousands etc. Sun Tzu wrote that "one is vertical, ten is horizontal."
The counting rod numerals system has place value and decimal numerals for computation, and was used widely by Chinese merchants, mathematicians and astronomers from Han dynasty to 16th century. In early civilizations, the Shang were able to express any numbers, however large with only 9 symbols and a counting board.
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. place-value], several centuries before such theory was understood in Europe, and while yet the science of numbers had scarcely dawned among the Arabs"
Cultural influences 
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 and Korea and were used in Vietnam 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 
- Chinese number gestures
- Japanese numerals
- Numbers in Chinese culture
- Chinese units of measurement
- Celestial stem
- List of numbers in Sinitic languages
- Note: Variant Chinese character of 肆, with a 镸 radical next to a 四 character. Not all browsers may be able to display this character, which forms a part of the Unicode CJK Unified Ideographs Extension A group.
- (Chinese) 1981 Gazette of the State Council of the People's Republic of China, No. 365, page 575, Table 7: SI prefixes
- The Shorter Science & Civilisation in China Vol 2, An abridgement by Colin Ronan of Joseph Needham's original text, Table 20, p6, Cambridge University Press ISBN 0-521-23582-0
- The Shorter Science & Civilisation in China Vol 2, An abridgement by Colin Ronan of Joseph Needham's original text, p5,Cambridge University Press ISBN 0-521-23582-0
- Chinese Wikisource 孫子算經: 先識其位，一從十橫，百立千僵，千十相望，萬百相當。
- The Shorter Science & Civilisation in China Vol 2, An abridgement by Colin Ronan of Joseph Needham's original text, p5,Cambridge University Press ISBN 0-521-23582-0
- Alexander Wylie, Jottings on the Sciences of the Chinese, North Chinese Herald, 1853, Shanghai
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