Chinese numerals

Chinese numerals are characters for writing numbers in Chinese. Today speakers of Chinese use three numeral systems: the ubiquitous Arabic numerals and two indigenous systems.

The more familiar indigenous system are Chinese characters that correspond to numerals in the spoken language. These are shared with other Sinospheric languages such as Japanese and Korean. Most people in China now use the Arabic system for convenience.

The other indigenous system are the Suzhou numerals, 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 before the 1990s, but have gradually been supplanted by the Arabic numerals.

Written numbers

Chinese and Arabic numerals may coexist, as on this kilometer marker: 1620 km on Hwy G209 (G二〇九)

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. 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.

Characters used to represent numbers

Paleolithic numerals

In the thirties of 20th century, archeologist Pei Wenzhong unearthed Upper Cave Man relics in Zhoukoudian,

Shang oracle numerals

Shang oracle bone numerals of 14th century B.C

Most Chinese numerals of later period were descendants from Shang dynasty oracle numerals of 14th century B.C. The oracle bone script numerals were found on tortoise shell and animal bones.

Bronze script

West Zhou dynasty 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

Main article: Counting rods

rod numeral place value from Yongle Encyclopedia

Japanese counting board with grids

Rod numerals also called counting rods. Counting rods 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 wrote that "one is vertical, ten is horizontal."

七	一	八	二	四
万	千	百	十	步

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 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 (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 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
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 贰 (S)	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 參 (S)	三	3	sān	also 弎 (obsolete financial), can be easily manipulated into 弌 (one) or 弍 (two). also 參(T) or 参(S) sān.
肆	四	4	sì	also 䦉 (obsolete financial)
伍	五	5	wǔ
陸 (T) or 陆 (S)	六	6	liù
柒	七	7	qī
捌	八	8	bā
玖	九	9	jiǔ
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).
佰	百	100	bǎi
仟	千	1,000	qiān
萬	萬 (T) or 万 (S)	104	wàn	Chinese numbers group by ten-thousands see Reading and transcribing numbers section below.
億	億 (T) or 亿 (S)	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.
	兩(T) or 两(S)	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(T) or 廿(S)	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》.

Large numbers

Similar to the long and short scales in the west, for numeral characters greater than 萬 (wàn), there have been four systems in ancient and modern usage:

Character (T)	億	兆	京	垓	秭	穰	溝	澗	正	載	Factor of increase
Character (S)	亿	兆	京	垓	秭	穰	沟	涧	正	载
Pinyin	yì	zhào	jīng	gāi	zǐ	ráng	gōu	jiàn	zhēng	zài
Alternative			經/经		杼	壤
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, as Megabyte or Migabits,the usage (representing 10¹²) is still consistent through Chinese communities, as well as Japan, Korea.

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 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

Numerals beyond 載 zài come from Buddhist texts in Sanskrit, but are mostly found in ancient texts.

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 (T)	Character (S)	Pinyin	Value	Notes
漠		mò	10−12	(Ancient Chinese) 皮 corresponds to the SI prefix pico-.
渺		miǎo	10−11	(Ancient Chinese)
埃		āi	10−10	(Ancient Chinese)
塵	尘	chén	10−9	(Ancient Chinese) 奈 (T) or 纳 (S) corresponds to the SI prefix nano-.
沙		shā	10−8	(Ancient Chinese)
纖	纤	qiān	10−7	(Ancient Chinese)
微		wēi	10−6	still in use, corresponds to the SI prefix micro.
忽		hū	10−5	(Ancient Chinese)
絲	丝	sī	10−4	(Ancient Chinese)
毫		háo	10−3	also 毛. still in use, corresponds to the SI prefix milli.
厘		lí	1/100	also 釐. still in use, corresponds to the SI prefix centi.
分		fēn	1/10	still in use, corresponds to the SI prefix deci.

SI prefixes

The translations for the SI prefixes in earlier days 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. For instance, 京 jīng was defined as giga, and 纖 xiān was defined as nano. This resulted in the creation of more values for each numeral.

By the time of "early 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.

SI Prefixes

Value	Symbol	English	Early translation	PRC standard	ROC standard
1024	Y	yotta-		堯 yáo	佑 yòu
1021	Z	zetta-		澤 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	太 tài	兆 zhào
109	G	giga-	京 jīng	吉 jí	吉 jí
106	M	mega-	兆 zhào	兆 zhào	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 yāo	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:

Number	Structure	Characters
		Mandarin	Cantonese	Chaozhou	Shanghainese
60	[6] [10]	六十	六十	六十	六十
20	[2] [10] or [20]	二十	二十 or 廿	二十	廿
200	[2] (èr) or (liǎng) [100]	二百 or 兩百	二百 or 兩百	兩百	兩百
2000	[2] (liǎng) [1000]	二千 or 兩千	二千 or 兩千	兩千	兩千
45	[4] [10] [5]	四十五	四十五 or 卌五	四十五	四十五
2,362	[2] [1,000] [3] [100] [6] [10] [2]	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
	Structure	Characters	Structure	Characters
14	[10] [4]	十四
12000	[1] [10000] [2] [1000]	一萬兩千	[1] [10000] [2] or [10000] [2]	一萬二 or 萬二
114	[1] [100] [1] [10] [4]	一百一十四	[1] [100] [10] [4]	一百十四
1158	[1] [1000] [1] [100] [5] [10] [8]	一千一百五十八	See note 1 below

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] (百十四).

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):

Number	Structure	Characters
12,345,678,902,345 (12,3456,7890,2345)	(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:

Number	Structure	Characters
205	[2] [100] [0] [5]	二百〇五
100,004 (10,0004)	[10] [10,000] [0] [4]	十萬〇四
10,050,026 (1005,0026)	(1005) [10,000] (26) or (1005) [10,000] (026)	一千〇五萬〇二十六 or 一千〇五萬二十六

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.

Fraction	Structure	Characters
2/3	[3] [parts of] [2]	三分之二
15/32	[3] [10] [2] [parts of] [10] [5]	三十二分之十五
1/3000	[3] [1000] [parts of] [1]	三千分之一
3 5/6	[3] [and] [6] [parts of] [5]	三又六分之五

Percentages are constructed similarly, using 百 (100) as the denominator. The 一 (one) before 百 is omitted.

Percentage	Structure	Characters
25%	[100] [parts of] [2] [10] [5]	百分之二十五
110%	[100] [parts of] [1] [100] [1] [10]	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.

Decimal expression	Structure	Characters
16.98	[10] [6] [point] [9] [8]	十六點九八
12345.6789	[1] [10000] [2] [1000] [3] [100] [4] [10] [5] [point] [6] [7] [8] [9]	一萬兩千三百四十五點六七八九
75.4025	[7] [10] [5] [point] [4] [0] [2] [5]	七十五點四〇二五
0.1	[0] [point] [1]	〇點一

Ordinal numbers

Ordinal numbers are formed by adding 第 ("sequence") before the number.

Ordinal	Structure	Characters
1st	[sequence] [1]	第一
2nd	[sequence] [2]	第二
82nd	[sequence] [8] [10] [2]	第八十二

Negative numbers

Negative numbers are formed by adding fù (simplified Chinese: 负; traditional Chinese: 負) before the number.

Number	Structure	Characters
-1158	[negative] [1] [1000] [1] [100] [5] [10] [8]	負一千一百五十八
-3 5/6	[negative] [3] [and] [6] [parts of] [5]	負三又六分之五
-75.4025	[negative] [7] [10] [5] [point] [4] [0] [2] [5]	負七十五點四〇二五

Suzhou numerals

Main article: 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

counting rod numerals

Main article: Counting rods

Ancient Chinese used positional decimal counting rod numerals for calculation since the Spring and Autumn period.

Hand gestures

Main article: Chinese number 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.

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. 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

External links

• Development of Hindu-Arabic and Traditional Chinese Arithmetic
• Chinese/English Number Converter
• Counting in Chinese - Caroline Baker - Counting in Chinese is as easy as Yi, Er, San!