Chinese numerals

Chinese numerals are characters for writing numbers in Chinese. Today, speakers of Chinese use three numeral systems: the ubiquitous system of Hindu-Arabic numerals, along with two ancient Chinese numeral systems. The Suzhou numerals (simplified Chinese: 苏州码子; traditional Chinese: 蘇州碼子; pinyin: Sūzhōu mǎzi) or huama (simplified Chinese: 花码; traditional Chinese: 花碼; pinyin: huāmǎ; lit. 'flowery or fancy numbers') system has gradually been supplanted by the Hindu-Arabic system in writing numbers. The character system is still used and roughly analogous to writing out a number in 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 Hindu-Arabic system.

The huama system, the only surviving variation of the rod numeral system, was once popular in use only in Chinese markets (e.g. in Hong Kong, before 1990). The character writing system is still in use when writing numbers in long form, such as on cheques to hinder forgery.

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

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. And since it reflects spoken language, it does not use the positional system as is done in Hindu-Arabic numerals, in the same way that spelling out numbers in English does not.

Numeral characters

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 叄拾 (30) and 伍仟 (5000).

S denotes Simplified, T denotes Traditional

Financial	Normal	Value	Notes
零	〇	0	〇 is an informal way to represent zero, but 零 is more commonly used, especially in schools.
壹	一	1 yi	also 弌 (obsolete) also 么(T) or 幺(S) yāo when used in phone numbers etc., see footnote 1.
貳(T) or 贰(S)	二	2 er	also 弍 (obsolete) also 兩(T) or 两(S) liǎng when used when placed before a measure word.
叄(T) or 叁(S)	三	3 san	also 弎 (obsolete) also 參(T) or 参(S) sān.
肆	四	4 si
伍	五	5 wu
陸(T) or 陆(S)	六	6 liu
柒	七	7 qi
捌	八	8 ba
玖	九	9 jiu
拾	十	10 shi	Although some people use 什 as financial, but it is not acceptable because it can be written over into 伍.
念 or 貳拾	廿 or 卄	20	卄 was rarely used, but still frequently used in spoken Chinese both used mostly on calendars (二十 is used). see constructing numbers below.
叄拾	卅	30	卅 was rarely used, but still frequently used in spoken Chinese used mostly on calendars (三十 is used).
肆拾	卌	40	卌 was hardly used (四十 is used).
佰	百	100
仟	千	1,000
萬	萬(T) or 万(S)	104	Chinese numbers group by ten-thousands see constructing numbers below.
億	億(T) or 亿(S)	108	(Ancient Chinese) Also: 105. see large number systems below.
兆		1012	(Ancient Chinese) Also: 106, 1016. Its usage has a dispute, see SI prefixes below.
京		1016	(Ancient Chinese) Also: 107, 1024, 1032. also 經(T) or 经(S).
垓		1020	(Ancient Chinese) Also: 108, 1032, 1064.
秭		1024	(Ancient Chinese) Also: 109, 1040, 10128. also 杼. 佑 (T) or 尧 (S) corresponds the SI prefix yotta.
穰		1028	(Ancient Chinese) Also: 1010, 1048, 10256. also 壤.
溝(T) or 沟(S)		1032	(Ancient Chinese) Also: 1011, 1056, 10512.
澗(T) or 涧(S)		1036	(Ancient Chinese) Also: 1012, 1064, 101024.
正		1040	(Ancient Chinese) Also: 1013, 1072, 102048.
載(T) or 载(S)		1044	(Ancient Chinese) Also: 1014, 1080, 104096.
極(T) or 极(S)		1048	(Buddhism)
恒河沙		1052	(Buddhism) The 3-character expression means roughly "Sand of the Ganges" and also appears in a Buddhist sutra; it is used in that context to convey a quantity equal to the number of grains of sand in the said river.
阿僧祇		1056	(Buddhism)
那由他		1060	(Buddhism)
不可思議(T) or 不可思议(S)		1064	(Buddhism) Literally translated as "unfathomable" or "unthinkable".
無量(T) or 无量(S)		1068	(Buddhism) Literally translated "without limit"
大數(T) or 大数(S)		1072	(Buddhism) Literally translated "big number"

么(T) or 幺(S) yāo, "the smallest", is used widely in mainland China as a replacement for yī in series of digits such as phone numbers, room numbers, etc. to prevent confusion between similar sounding words. It is never used in counting, nor is it used in Taiwan (except for soldiers in the ROC military, the police force, and the emergency telephone number 119 for calling a fire department or requesting an ambulance) or Hong Kong and Macau (except when communicating in Standard Mandarin).

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

Constructing 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 used rather than 二 (èr) for all numbers greater than 200 with the "2" numeral. 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]	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]	一萬二千	[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), 10000 × yì (億) = zhào (兆). 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]	二百零五
100,004 (10,0004)	[10] [10,000] [0] [4]	十萬零四
10,050,026 (1005,0026)	(1005) [10,000] (26) or (1005) [10,000] (026)	一千零五萬零二十六 or 一千零五萬二十六

Large number systems

For numeral characters greater than 萬 (wàn), there have been four systems in ancient and modern usage:

System	億 yì	兆 zhào	京 jīng	垓 gāi	秭 zǐ	穰 ráng	溝 gōu	澗 jiàn	正 zhēng	載 zài	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 (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, Korea. However, most people do not recognize numerals beyond 億 yì (10⁸) and dictionary definitions on the words of larger number may not be consistent (except Korea where 兆zhào and 京jīng are frequently used) The numerals beyond 載 jí come from Buddhist texts in Sanskrit, but these "Buddhist numerals" have become "ancient usage".

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 ("again"), 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] [again] [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]	一十六點九八
12345.6789	[1] [10000] [2] [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]	七十五點四零二五
0.1	[0] [point] [1]	零點一

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 負 (traditional) 负 (simplified) ("negative") 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] [again] [6] [parts of] [5]	負三又六分之五
-75.4025	[negative] [7] [10] [5] [point] [4] [0] [2] [5]	負七十五點四零二五

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, the Taiwanese government 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		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	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

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 (蘇州) or huāmǎ (花碼) 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. In the huāmǎ system, special symbols are used for digits instead of the Chinese characters. The digits are positional. When written horizontally, the numerical value is written in two rows. For example:

〤	〇	〢	二
拾	元

The top row contains the numeric symbols, for example, 〤〇〢二 stands for 4022. The bottom row consists of one or more Chinese characters that represents the unit of the first digit in the first row. The first part in the bottom row indicates the order of the first digit in the top row, e.g. qiān (千) for thousand, bái (百) for hundred, shí (拾) for ten, blank for one etc. The second part denotes the unit of measurement, such as yuán (元 for dollar) or máo (毫 or 毛 for 10 cents) or xiān (仙 for 1 cent) or lǐ (里 for the Chinese mill) or any other measurement unit. If the characters shí yuán (拾元, "10 dollars") are below the digits 〤〇〢二, it is then read as forty dollars and twenty two cents. Notice that the decimal point is implicit when the first digit '4' is set at the 'ten' position. This is very similar to the modern scientific notation for floating point numbers where the significant digits are represented in the mantissa and the order of magnitude is specified in the exponent. Also, the unit of mesurement, with the first digit indicater, is usually aligned to the middle of the "numbers" row.

When written vertically, the above example is written thus:

拾	〤
元	〇
	〢
	二

The digits of the Suzhou numerals are defined between U+3021 and U+3029 in Unicode. According to the Unicode standard version 3.0, these characters are called Hangzhou style numerals. This indicates that it is not used only by Cantonese in Hong Kong. In the Unicode standard 4.0, an erratum was added which stated:

The Suzhou numerals (simplified Chinese: 苏州码子; traditional Chinese: 蘇州碼子; pinyin: Sūzhōu mǎzi) are special numeric forms used by traders to display the prices of goods. The use of "HANGZHOU" in the names is a misnomer.

All references to "Hangzhou" in the Unicode standard have been corrected to "Suzhou" except for the character names themselves, which cannot be changed once assigned, according to the Unicode Stability Policy. (This policy allows software to use the names as unique identifiers.)

Zero is represented by the character for zero (〇). Leading and trailing zeros are unnecessary in this system. Additional characters representing 10, 20, 30 and 40 exist: 十, 卄, 卅, 卌.

Unicode for Suzhou numerals

Number	"Hangzhou"		CJK Ideographs
	Character	Unicode	Character	Unicode
0			〇	U+3007
1	〡	U+3021	一	U+4E00
2	〢	U+3022	二	U+4E8C
3	〣	U+3023	三	U+4E09
4	〤	U+3024
5	〥	U+3025
6	〦	U+3026
7	〧	U+3027
8	〨	U+3028
9	〩	U+3029

For those who cannot see the Unicode glyphs in the web browser, an image with the appearance of these digits is shown in the right. Some web browsers, such as IE 5.5, display the character for 9 incorrectly as the "fǎn wén", or reverse "wén" radical (夂 & 攵 & 夊 & 文), click here to see the correct graphic glyph.

The digits 1 to 3 come in the vertical and horizontal version so that they can alternate if these digits are next to each other. The first digit usually use the vertical version. e.g. 21 is written as 〢一 instead of 〢〡 which can be confused with 3 (〣).

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

• Japanese numerals
• Numbers in Chinese culture
• Chinese units of measurement

External links

• Chinese/English Number Converter
• Learn how to write Chinese numbers free PDF for download