Chinese numerals
Encyclopedia
Chinese numerals are characters for writing number
Number
A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers....

s in Chinese
Chinese language
The Chinese language is a language or language family consisting of varieties which are mutually intelligible to varying degrees. Originally the indigenous languages spoken by the Han Chinese in China, it forms one of the branches of Sino-Tibetan family of languages...

. Today speakers of Chinese use three numeral system
Numeral system
A numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....

s:
the ubiquitous Arabic numerals
Arabic numerals
Arabic numerals or Hindu numerals or Hindu-Arabic numerals or Indo-Arabic numerals are the ten digits . They are descended from the Hindu-Arabic numeral system developed by Indian mathematicians, in which a sequence of digits such as "975" is read as a numeral...

 and two indigenous systems.

The more familiar indigenous system are Chinese character
Chinese character
Chinese characters are logograms used in the writing of Chinese and Japanese , less frequently Korean , formerly Vietnamese , or other languages...

s that correspond to numerals in the spoken language
Number names
In linguistics, number names are specific words in a natural language that represent numbers.In writing, numerals are symbols also representing numbers...

. These are shared with other Sinospheric languages
Sinosphere
In areal linguistics, Sinosphere refers to a grouping of countries and regions that are currently inhabited with a majority of Chinese population or were historically under Chinese cultural influence...

 such as Japanese and Korean. Most people in China now use the Arabic system for convenience.

The other indigenous system are the Suzhou numerals
Suzhou numerals
The Suzhou numerals or huama is a numeral system used in China before the introduction of Arabic numerals.-History:The Suzhou numeral system is the only surviving variation of the rod numeral system. The rod numeral system is a positional numeral system used by the Chinese in mathematics...

, or huama, a positional system. They are 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
Hong Kong
Hong Kong is one of two Special Administrative Regions of the People's Republic of China , the other being Macau. A city-state situated on China's south coast and enclosed by the Pearl River Delta and South China Sea, it is renowned for its expansive skyline and deep natural harbour...

 before the 1990s, but have gradually been supplanted by the Arabic numerals.

Written numbers

The Chinese character numeral system consists of the Chinese characters used by the Chinese written language
Chinese written language
Written Chinese comprises Chinese characters used to represent the Chinese language, and the rules about how they are arranged and punctuated. Chinese characters do not constitute an alphabet or a compact syllabary...

 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. Since it reflects spoken language, it does not use the positional system as is done in Arabic numerals
Arabic numerals
Arabic numerals or Hindu numerals or Hindu-Arabic numerals or Indo-Arabic numerals are the ten digits . They are descended from the Hindu-Arabic numeral system developed by Indian mathematicians, in which a sequence of digits such as "975" is read as a numeral...

, in the same way that spelling out numbers in English does not.

Paleolithic numerals

In the thirties of 20th century, archeologist Pei Wenzhong
Pei Wenzhong
Pei Wenzhong was a Chinese paleontologist, archaeologist and anthropologist. Professor Pei is considered the founding father of Chinese anthropology....

 unearthed Upper Cave Man relics in Zhoukoudian
Zhoukoudian
Zhoukoudian or Choukoutien is a cave system in Beijing, China. It has yielded many archaeological discoveries, including one of the first specimens of Homo erectus, dubbed Peking Man, and a fine assemblage of bones of the gigantic hyena Pachycrocuta brevirostris...

,

Shang oracle numerals


Most Chinese numerals of later period were descendants from Shang dynasty oracle numerals of 14th century B.C. The oracle bone script
Oracle bone script
Oracle bone script refers to incised ancient Chinese characters found on oracle bones, which are animal bones or turtle shells used in divination in Bronze Age China...

 numerals were found on tortoise shell and animal bones.

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

Rod numerals also called counting rods. Counting rods
Counting rods
Counting rods are small bars, typically 3–14 cm long, used by mathematicians for calculation in China, Japan, Korea, and Vietnam. They are placed either horizontally or vertically to represent any number and any fraction....

 represent digits by the number of rods, and the perpendicular rod represents five. To avoid confusion, vertical and horizontal forms are alternately used. Generally, vertical rod numbers are used for the position for the units, hundreds, ten thousands, etc., while horizontal rod numbers are used for the tens, thousands, hundred thousands etc. Sun Tzu
Sun Tzu (mathematician)
Sun Tzu or Sun Zi was a Chinese mathematician, flourishing between the 3rd and the 5th century AD.Interested in astronomy and trying to develop a calendar, he investigated Diophantine equations...

 wrote that "one is vertical, ten is horizontal."


Counting rod numerals system is place value decimal numerals for computation, used widely by Chinese merchants, mathematicians and astronomers from Han dynasty to 16th century. In early civilizations, only the Shang Chinese were able to express any numbers, however large with only 9 symbols and a counting board

Christian missionary to China, Alexander Wylie
Alexander Wylie
Alexander Wylie , British Protestant 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 were carried out by means of counting rods, and "the written character is evidently a rude presentation of these". After introduced 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"

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 . 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 叁拾 (30) and 伍仟 (5000). They are sometimes also referred to as "banker's numerals" or "anti-fraud numerals." For the same reason, rod numerals were never used in commercial records.

A reformed Chinese abacus with red beads signifying ones units for each group. Number indicated above is 1,234,567.89
Rod calculus was the computing mechanism in China from antiquity up to Ming dynasty, when it was replaced by the more portable and much quicker abacus. However, the abacus retains all the main feature of counting rods, a rod became a bead, an overhead rod became an overhead bead top of a partion bar, there is exact 1 to 1 correspondence between a rod numeral and abacus numeral, In a sense, the counting rods mutated into abacus, in other words, the ancient Chinese positional decimal system took a new form and lives on in abacus. Like the counting rods, a blank on a position on abacus represents 0.

T denotes Traditional, S denotes Simplified.
Financial Normal Value Pīnyīn Notes
0
0 (number)
0 is both a numberand the numerical digit used to represent that number in numerals.It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems...

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
CJK Unified Ideographs
The Chinese, Japanese and Korean scripts share a common background. In the process called Han unification the common characters were identified, and named "CJK Unified Ideographs"...

.
1 also 弌 (obsolete financial), can be easily manipulated into 弍 (two) or 弎 (three).
貳 (T) or
贰 (S)
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.
叄 (T) or
叁 (S)
3 sān also 弎 (obsolete financial), can be easily manipulated into 弌 (one) or 弍 (two).
also 參(T) or 参(S) sān.
4 also 䦉 (obsolete financial)
5  
陸 (T) or
陆 (S)
6 liù  
7  
8  
9 jiǔ  
10
10 (number)
10 is an even natural number following 9 and preceding 11.-In mathematics:Ten is a composite number, its proper divisors being , and...

shí Although some people use 什 as financial, it is not ideal because it can be easily manipulated into 伍 (five) or 仟 (thousand).
100
100 (number)
100 is the natural number following 99 and preceding 101.-In mathematics:One hundred is the square of 10...

bǎi  
1,000 qiān
萬 (T) or
万 (S)
104
10000 (number)
10000 is the natural number following 9999 and preceding 10001.-Name:Many languages have a specific word for this number: In English it is myriad, in Ancient Greek , in Aramaic , in Hebrew רבבה , in Chinese , in Japanese [man], in Korean [man], and in Thai หมื่น [meun]...

wàn Chinese numbers group by ten-thousands
see Reading and transcribing numbers section below.
億 (T) or
亿 (S)
108 See large numbers section below.

Characters with regional usage

Financial Normal Value Pinyin (Mandarin) Standard alternative Notes
1 yāo 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
Taiwan
Taiwan , also known, especially in the past, as Formosa , is the largest island of the same-named island group of East Asia in the western Pacific Ocean and located off the southeastern coast of mainland China. The island forms over 99% of the current territory of the Republic of China following...

, it is only used by soldier
Soldier
A soldier is a member of the land component of national armed forces; whereas a soldier hired for service in a foreign army would be termed a mercenary...

s, police
Police
The police is a personification of the state designated to put in practice the enforced law, protect property and reduce civil disorder in civilian matters. Their powers include the legitimized use of force...

, and emergency service
Emergency service
Emergency services are organizations which ensure public safety and health by addressing different emergencies. Some agencies exist solely for addressing certain types of emergencies whilst others deal with ad hoc emergencies as part of their normal responsibilities...

s. This usage is not observed in Cantonese except for 十三幺 (a special winning hand) in Mahjong
Mahjong
Mahjong, sometimes spelled Mah Jongg, is a game that originated in China, commonly played by four players...

.
兩(T) or
两(S)
2 liǎng 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.
10
10 (number)
10 is an even natural number following 9 and preceding 11.-In mathematics:Ten is a composite number, its proper divisors being , and...

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(T) or
廿(S)
20
20 (number)
20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.-In mathematics:*20 is the basis for vigesimal number systems....

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.
30
30 (number)
30 is the natural number following 29 and preceding 31.-In mathematics:30 is the sum of the first four squares, which makes it a square pyramidal number.It is a primorial and is the smallest Giuga number....

三十 The written form is still used to abbreviate date references in Chinese. For example, May 30 Movement
May 30 Movement
The May Thirtieth Movement was a labor and anti-imperalist movement during the middle-period of the Republic of China era. It began when Shanghai Municipal Police officers opened fire on Chinese protesters in Shanghai's International Settlement...

 (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.
40
40 (number)
40 is the natural number following 39 and preceding 41.Despite being related to the word "four" , 40 is spelled "forty", and not "fourty"...

四十 Spoken form is still used in various dialects of Chinese, albeit very rare, as well as historical writings written in Classical Chinese
Classical Chinese
Classical Chinese or Literary Chinese is a traditional style of written Chinese based on the grammar and vocabulary of ancient Chinese, making it different from any modern spoken form of 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".
200
200 (number)
200 is the natural number following 199 and preceding 201.The number appears in the Padovan sequence, preceded by 86, 114, 151 ....

二百 Very rarely used, one common example is the literature 《皕宋樓》.

Large numbers

Similar to the long and short scales
Long and short scales
The long and short scales are two of several different large-number naming systems used throughout the world for integer powers of ten. Many countries, including most in continental Europe, use the long scale whereas most English-speaking countries use the short scale...

  in the west, for numeral characters greater than 萬 (wàn), there have been four systems in ancient and modern usage:
Character (T) Factor of increase
Character (S) 亿
Pinyin zhào jīng gāi ráng gōu jiàn zhēng zài
Alternative 經/经
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 (萬 wàn) times the previous.
3 108 1016 1024 1032 1040 1048 1056 1064 1072 1080 Each numeral is 108 (萬萬 wànwàn) times the previous.
4 108 1016 1032 1064 10128 10256 10512 101024 102048 104096 Each numeral is the square of the previous.

In modern Chinese, only the second system is used in expressing numbers. Although there is some dispute on the value of 兆 zhào, the usage (representing 1012) is still consistent through Chinese communities, as well as Japan
Japanese numerals
The system of Japanese numerals is the system of number names used in the Japanese language. The Japanese numerals in writing are entirely based on the Chinese numerals and the grouping of large numbers follow the Chinese tradition of grouping by 10,000...

, Korea
Korean numerals
The Korean language has two regularly used sets of numerals, a native Korean system and Sino-Korean system.-Construction:For both native and Sino- Korean numerals, the teens are represented by a combination of tens and the ones places...

.

One example of ambiguity is 兆 (zhào), which traditionally means 1012 but is also used for 106 in information technology in recent years (esp. in mainland China). To avoid problems arising from the ambiguity, the PRC
People's Republic of China
China , officially the People's Republic of China , is the most populous country in the world, with over 1.3 billion citizens. Located in East Asia, the country covers approximately 9.6 million square kilometres...

 government never uses this character in official documents, but uses 万亿 (wànyì) instead. (the ROC
Republic of China
The Republic of China , commonly known as Taiwan , is a unitary sovereign state located in East Asia. Originally based in mainland China, the Republic of China currently governs the island of Taiwan , which forms over 99% of its current territory, as well as Penghu, Kinmen, Matsu and other minor...

 government in Taiwan
Taiwan
Taiwan , also known, especially in the past, as Formosa , is the largest island of the same-named island group of East Asia in the western Pacific Ocean and located off the southeastern coast of mainland China. The island forms over 99% of the current territory of the Republic of China following...

 uses 兆 (zhào) to mean 1012 in official documents.)

Numbers from Buddhism

Numerals beyond 載 zài come from Buddhist texts
Buddhist texts
Buddhist texts can be categorized in a number of ways. The Western terms "scripture" and "canonical" are applied to Buddhism in inconsistent ways by Western scholars: for example, one authority refers to "scriptures and other canonical texts", while another says that scriptures can be categorized...

 in Sanskrit
Sanskrit
Sanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism, Jainism and Buddhism.Buddhism: besides Pali, see Buddhist Hybrid Sanskrit Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand...

, but are mostly found in ancient texts.
Character (T) Character (S) Pinyin Value Notes
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
Buddhist texts
Buddhist texts can be categorized in a number of ways. The Western terms "scripture" and "canonical" are applied to Buddhism in inconsistent ways by Western scholars: for example, one authority refers to "scriptures and other canonical texts", while another says that scriptures can be categorized...

 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
Order of magnitude
An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...

 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.

{| class="wikitable"
|-
!width="70"|Character (T)
!width="70"|Character (S)
!width="60"|Pinyin
! Value
! Notes
|-
| colspan="2" style="text-align:center;"|漠
|align=center|mò
|align=center|10−12
|(Ancient Chinese)
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