Chinese numerals

Numeral systems by culture
Hindu-Arabic numerals
Western Arabic; Indian family; Khmer	Eastern Arabic; Brahmi; Thai
East Asian numerals
Chinese; Suzhou	Counting rods; Mongolian
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Other systems
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	2, 4, 8, 16, 32, 64
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Chinese numerals are characters for writing numbers in Chinese. Today, speakers of Chinese use three numeral systems: the ubiquitous system of Arabic numerals, along with two ancient Chinese numeral systems.

One such system is the Suzhou numerals or huama system. It has gradually been supplanted by the Arabic system in writing numbers. It is the only surviving variation of the rod numeral system; this system has been popular only in Chinese markets, such as those in Hong Kong before the 1990s.

The other Chinese numeral system is the written numbers system. It is still in use when writing numbers in long form, such as on cheques to hinder forgery. This character system is roughly analogous to spelling out a number in English text. The Chinese character system can be classified as part of the language, but it still counts as a number system. Most people in China now use the Arabic system for convenience.

Individual Chinese characters in this article link to their dictionary entries.

[edit] Written numbers

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.

[edit] Characters used to represent numbers

[edit] 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 (大寫 in traditional Chinese, 大写 in simplified Chinese). 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).

S denotes Simplified, T denotes Traditional

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.
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.
叄(T) or 叁(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
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 acceptable because it can be easily manipulated into 伍 or 仟.
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.

[edit] Characters with regional usage

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.
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", "两千二百二十二" or even "两千两百二十二" 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 or 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 (五卅运动). Spoken form is still used in various dialects of Chinese. See Reading and transcribing numbers section below.
卌	40	xì	四十	Spoken form is still used in various dialects of Chinese, albeit very rare.
皕	200	bì	二百	Very rarely used, one common example is the literature 《皕宋楼》.

[edit] Large numbers

Similar to the long and short scales in the west, for numeral characters greater than 万 (wàn), there have been four systems in ancient and modern usage:

System	亿 yì	兆 zhào	京 jīng	垓 gāi	秭 zǐ	穰 ráng	沟 gōu	涧 jiàn	正 zhēng	载 zài	Factor of increase
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 (万 wàn) times the previous.
3	10⁸	10¹⁶	10²⁴	10³²	10⁴⁰	10⁴⁸	10⁵⁶	10⁶⁴	10⁷²	10⁸⁰	Each numeral is 10⁸ (万万 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, 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.)

[edit] Numbers from Buddhism

The numerals beyond 载 zài come from Buddhist texts in Sanskrit, but these "Buddhist numerals" have become "ancient usage".

Name	Value	Notes
極(T) or 极(S)	10⁴⁸
恆河沙(T) or 恒河沙(S)	10⁵²	Literally means "Sands of the Ganges", a metaphor used in number of Buddhist texts to convey a quantity equal to the number of grains of sand in the Ganges river.
阿僧祇	10⁵⁶	From Sanskrit Asaṃkhyeya
那由他	10⁶⁰	From Sanskrit Nayuta
不可思議(T) or 不可思议(S)	10⁶⁴	Literally translated as "unfathomable" or "unthinkable".
無量(T) or 无量(S)	10⁶⁸	Literally translated "without limit"
大數(T) or 大数(S)	10⁷²	Literally translated "big number"

[edit] 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	Value	Notes
漠	10^-12	(Ancient Chinese) 皮 corresponds to the SI prefix pico.
渺	10^-11	(Ancient Chinese)
埃	10^-10	(Ancient Chinese)
尘	10^-9	(Ancient Chinese) 奈 (T) or 纳 (S) corresponds to the SI prefix nano.
沙	10^-8	(Ancient Chinese)
纤	10^-7	(Ancient Chinese)
微	10^-6	still in use, corresponds to the SI prefix micro.
忽	10^-5	(Ancient Chinese)
丝	10^-4	(Ancient Chinese)
毫	1/1,000	also 毛. still in use, corresponds to the SI prefix milli.
厘	1/100	also 釐. still in use, corresponds to the SI prefix centi.
分	1/10	still in use, corresponds to the SI prefix deci.

[edit] 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, 纤, 沙, 尘, 渺) were defined as translations for the SI prefixes. For instance, 京 jīng was defined as giga, and 纤 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 百万 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		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	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	hecta	百 bǎi	百 bǎi	百 bǎi
10¹	da	deca	十 shí	十 shí	十 shí
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	纤 xiān	纳 nà	奈 nài
10^-12	p	pico	沙 shā	皮 pí	皮 pí
10^-15	f	femto	尘 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

[edit] Reading and transcribing numbers

[edit] 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 两 (liǎng) is used rather than 二 (èr) for all numbers greater than 200 with the "2" numeral. Use of both 两 (liǎng) or 二 (èr) are acceptable for the number 200.(NOTE, 二 is not appropriate in the common usage of 250, namely 二百五.) 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), 两 (no⁶) is used to represent the "2" numeral in all numbers from 200 onwards. Thus:

Number	Structure	Characters
Number	Structure	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 两百	二百 or 两百	两百	两百
2000	[2] (liǎng) [1000]	二千 or 两千	二千 or 两千	两千	两千
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]	两千三百六十二	二千三百六十二	两千三百六十二	两千三百六十二

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
Number	Structure	Characters	Structure	Characters
14	[10] [4]	十四
12000	[1] [10000] [2] [1000]	一万两千	[1] [10000] [2] or [10000] [2]	一万二 or 万二
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:

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 (万) = yì (亿). 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)	十二万三千四百五十六亿七千八百九十万两千三百四十五

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]	十万〇四
10,050,026 (1005,0026)	(1005) [10,000] (26) or (1005) [10,000] (026)	一千〇五万〇二十六 or 一千〇五万二十六

[edit] 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 點 (traditional) or 点 (simplified) ("point"), 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]	十六点九八
12345.6789	[1] [10000] [2] [1000] [3] [100] [4] [10] [5] [point] [6] [7] [8] [9]	一万两千三百四十五点六七八九
75.4025	[7] [10] [5] [point] [4] [0] [2] [5]	七十五点四〇二五
0.1	[0] [point] [1]	〇点一

[edit] 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

[edit] Negative numbers

Negative numbers are formed by adding 負 (traditional) 负 (simplified) ("negative") before the number.

Number	Structure	Characters
-1158	[negative] [1] [1000] [1] [100] [5] [10] [8]	负一千一百五十八
-3 ⁵/₆	[negative] [3] [and] [6] [parts of] [5]	负三又六分之五
-75.4025	[negative] [7] [10] [5] [point] [4] [0] [2] [5]	负七十五点四〇二五

[edit] 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 (苏州) or huāmǎ (花码) 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.

[edit] 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.

[edit] 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.

[edit] See also

[edit] References

[edit] External links