Chinese numerals

Chinese numerals are words and characters used to denote numbers in written Chinese.

Today, speakers of Chinese languages use three written numeral systems: the system of Arabic numerals used worldwide, and two indigenous systems. The more familiar indigenous system is based on Chinese characters that correspond to numerals in the spoken language. These may be shared with other languages of the Chinese cultural sphere such as Korean, Japanese, and Vietnamese. Most people and institutions in China primarily use the Arabic or mixed Arabic-Chinese systems for convenience, with traditional Chinese numerals used in finance, mainly for writing amounts on cheques, banknotes, some ceremonial occasions, some boxes, and on commercials.

The other indigenous system consists of the Suzhou numerals, or huama, a positional system, the only surviving form of the rod numerals. These were once used by Chinese mathematicians, and later by merchants in Chinese markets, such as those in Hong Kong until the 1990s, but were gradually supplanted by Arabic numerals.

Basic counting in Chinese

File:Muyu-G209-1620km-5469-crop.jpg

Chinese and Arabic numerals may coexist, as on this kilometer marker: Template:Convert on Hwy G209 (Template:Zhi)

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.

Ordinary numerals

There are characters representing the numbers zero through nine, and other characters representing larger numbers such as tens, hundreds, thousands, ten thousands and hundred millions. There are two sets of characters for Chinese numerals: one for everyday writing, known as Template:Zhi (Template:Zhi), and one for use in commercial, accounting or financial contexts, known as Template:Zhi (Template:Zhi or 'capital numbers'). The latter were developed by Wu Zetian (Template:Floruit) and were further refined by the Hongwu Emperor (Template:Floruit). They 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 the everyday characters Template:Zhi (30) to Template:Zhi (5000) just by adding a few strokes. That would not be possible when writing using the financial characters Template:Zhi (30) and Template:Zhi (5000). They are also referred to as "banker's numerals" or "anti-fraud numerals". For the same reason, rod numerals were never used in commercial records.

Value	Financial		Ordinary		Pinyin (Mandarin)	Jyutping (Cantonese)	Tâi-lô (Hokkien)	Wugniu [1](Shanghainese)	Notes
	Traditional	SimplifiedTemplate:Rp	Traditional	Simplified
0	Template:Zhi		Template:Zhi or Template:Zhi		Template:Zhi	Template:Zhi	Template:Zhi	Template:Transliteration	Usually Template:Zhi is preferred, but in some areas, 〇 may be a more common informal way to represent zero. The original Chinese character is Template:Zhi or Template:Zhi, Template:Zhi is referred as remainder something less than 1 yet not nil [[[:Template:Zhi]]] referred. The traditional Template:Zhi is more often used in schools. In Unicode, 〇 is treated as a Chinese symbol or punctuation, rather than a Chinese ideograph.
1	Template:Zhi		Template:Zhi		Template:Zhi	Template:Zhi	Template:Zhi	Template:Transliteration	Also Template:Zhi (obsolete financial), can be easily manipulated into Template:Zhi or Template:Zhi.
2	Template:Zhi	Template:Zhi	Template:Zhi		Template:Zhi	Template:Zhi	Template:Zhi	Template:Transliteration	Also Template:Zhi (obsolete, financial), can be easily manipulated into Template:Zhi or Template:Zhi. Also Template:Zhi.
3	Template:Zhi	Template:Zhi	Template:Zhi		Template:Zhi	Template:Zhi	Template:Zhi	Template:Transliteration	Also Template:Zhi (obsolete financial), which can be easily manipulated into Template:Zhi or Template:Zhi.
4	Template:Zhi		Template:Zhi		Template:Zhi	Template:Zhi	Template:Zhi	Template:Transliteration	Also Template:Zhi (obsolete financial).Template:Refn
5	Template:Zhi		Template:Zhi		Template:Zhi	Template:Zhi	Template:Zhi	Template:Transliteration	Template:N/A
6	Template:Zhi	Template:Zhi	Template:Zhi		Template:Zhi	Template:Zhi	Template:Zhi	Template:Transliteration	Template:N/A
7	Template:Zhi		Template:Zhi		Template:Zhi	Template:Zhi	Template:Zhi	Template:Transliteration	Template:N/A
8	Template:Zhi		Template:Zhi		Template:Zhi	Template:Zhi	Template:Zhi	Template:Transliteration	Template:N/A
9	Template:Zhi		Template:Zhi		Template:Zhi	Template:Zhi	Template:Zhi	Template:Transliteration	Template:N/A
10	Template:Zhi		Template:Zhi		Template:Zhi	Template:Zhi	Template:Zhi	Template:Transliteration	Although some people use Template:Zhi as financial, it is not ideal because it can be easily manipulated into Template:Zhi or Template:Zhi.
100	Template:Zhi		Template:Zhi		Template:Zhi	Template:Zhi	Template:Zhi	Template:Transliteration	Template:N/A
1,000	Template:Zhi		Template:Zhi		Template:Zhi	Template:Zhi	Template:Zhi	Template:Transliteration	Template:N/A
104	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Transliteration	Chinese numbers group by ten-thousands; see Reading and transcribing numbers below.
108	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Transliteration	For variant meanings and words for higher values, see Large numbers below.

1. ^ Wugniu is a pan-Wu romanization scheme, but the exact romanization depends on the variety. The romanization listed here is specifically for Shanghainese.

Regional usage

Financial	Normal	Value	Pinyin	Standard alternative	Notes
		0	Template:Zhi		Historically, the use of for 'zero' predates . This is now archaic in most varieties of Chinese, but it is still used in most of Southern Min.
		0	Template:Zhi		Literally 'a hole', is analogous to the shape of Template:Angbr and Template:Angbr, it is used to unambiguously pronounce #0 in radio communication.
		1	Template:Zhi		Literally 'the smallest', it is used to unambiguously pronounce #1 in radio communication. This usage is not observed in Cantonese except for Template:Zhi, which refers to a special winning hand in mahjong.
		1	Template:Zhi		In most Min varieties, there are two words meaning 'one'. For example, in Hokkien, Template:Zhi is used before a classifier: 'one person' is Template:Zhi, not Template:Zhi. In written Hokkien, Template:Zhi is often used for both Template:Zhi and Template:Zhi, but some authors differentiate, writing Template:Zhi for Template:Zhi and Template:Zhi for Template:Zhi.
	Template:Zhi	2	Template:Zhi		Used instead of Template:Zhi before a classifier. For example, 'two people' is Template:Zhi, not Template:Zhi. However, in some lects such as Shanghainese, Template:Zhi is the generic term used for two in most contexts, such as Template:Zhi and not Template:Zhi. It appears where 'a pair of' might in English, but Template:Zhi is always used in such cases. It is also used for numbers, with usage varying from dialect to dialect, even person to person. For example, '2222' can be read as Template:Zhi, Template:Zhi, or even Template:Zhi in Mandarin. It is used to unambiguously pronounce #2 in radio communication.
	Template:Zhi	2	Template:Zhi		In regional dialects of Northeastern Mandarin, Template:Zhi represents a "lazy" pronunciation of Template:Zhi within the local dialect. It can be used as an alternative for Template:Zhi, e.g. Template:Zhi, as opposed to Template:Zhi. A measure word never follows Template:Zhi.
		3	Template:Zhi		In regional dialects of Northeastern Mandarin, Template:Zhi represents a "lazy" pronunciation of three within the local dialect. It can be used as a general number to represent 'three', e.g.Template:Zhi; Template:Zhi, or as an alternative for Template:Zhi, e.g. Template:Zhi, as opposed to Template:Zhi). Regardless of usage, a measure word never follows Template:Zhi.
		7	Template:Zhi		Literally 'a turn' or 'a walking stick' and is analogous to the shape of Template:Angbr and Template:Zhi, it is used to unambiguously pronounce #7 in radio communication.
		9	Template:Zhi		Literally 'a hook' and is analogous to the shape of Template:Angbr, it is used to unambiguously pronounce #9 in radio communication.
		10	Template:Zhi		In spoken Cantonese, Template:Zhc can be used in place of Template:Zhi when it is used in the middle of a number, preceded by a multiplier and followed by a ones digit, e.g. Template:Zhi '63', it is not used by itself to mean 10. This usage is not observed in Mandarin.
		20	Template:Zhi	Template:Zhi	A contraction of Template:Zhi. 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 spoken Cantonese, Template:Zhc can be used in place of Template:Zhi when followed by another digit such as in numbers 21–29 (e.g. Template:Zhi '23', a measure word, e.g. Template:Zhi, a noun, or in a phrase like Template:Zhi 'twenty-something'. It is not used by itself to mean 20. Template:Zhi is still used in place of Template:Zhi in Southern Min and Wu. is a rare variant.
		30	Template:Zhi	Template:Zhi	A contraction of Template:Zhi. The written form is still used to abbreviate date references in Chinese. For example, May 30 Movement (Template:Zhi). The spoken form is still used in various dialects of Chinese. In spoken Cantonese, Template:Zhi can be used in place of Template:Zhi when followed by another digit such as in numbers 31–39, a measure word (e.g. Template:Zhi), a noun, or in phrases like Template:Zhi 'thirty-something'. It is not used by itself to mean 30. When spoken Template:Zhi is pronounced as Template:Zhi. Thus Template:Zhi '31', is pronounced as Template:Transliteration.
		40	Template:Zhi	Template:Zhi	A contraction of Template:Zhi. Found in historical writings written in Literary Chinese. Spoken form is still used in various dialects of Chinese, albeit very rare. See Reading and transcribing numbers section below. In spoken Cantonese Template:Zhi can be used in place of Template:Zhi when followed by another digit such as in numbers 41–49, a measure word (e.g. Template:Zhi), a noun, or in phrases like Template:Zhi 'forty-something', it is not used by itself to mean 40. When spoken, Template:Zhi is pronounced as Template:Zhi. Thus Template:Zhi, is pronounced as Template:Transliteration. Similarly, in Southern Min 41 can be referred to as Template:Zhi.
		200	Template:Zhi	Template:Zhi	Very rarely used; one example is in the name of a library in Huzhou, Template:Zhi.

Powers of 10

Large numbers

For numbers larger than 10,000, similarly 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, Template:Zhi. In modern Chinese, only the second system is used, in which the same ancient names are used, but each represents a myriad, Template:Zhi times the previous:

Character	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Factor of increase
Character (S)	Template:Zhi	Template:Zhi						Template:Zhi	Template:Zhi		Template:Zhi
Pinyin	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi
Jyutping	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi
Tai Lo	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi
Wugniu	Template:Transliteration	Template:Transliteration	Template:Transliteration	Template:Transliteration	Template:Transliteration	Template:Transliteration	Template:Transliteration	Template:Transliteration	Template:Transliteration	Template:Transliteration	Template:Transliteration
Alternative				Template:Zhi		Template:Zhi	Template:Zhi
Rank	1	2	3	4	5	6	7	8	9	10	11	=n
"short scale" (Template:Zhi)	104	105	106	107	108	109	1010	1011	1012	1013	1014	=10n+3 Each numeral is 10 (Template:Zhi) times the previous.
"myriad scale" (Template:Zhi, current usage)	104	108	1012	1016	1020	1024	1028	1032	1036	1040	1044	=104n Each numeral is 10,000 (Template:Zhi) times the previous.
"mid-scale" (Template:Zhi)	104	108	1016	1024	1032	1040	1048	1056	1064	1072	1080	=108(n-1) Starting with Template:Zhi, each numeral is 108 (Template:Zhi) times the previous.
"long scale" (Template:Zhi)	104	108	1016	1032	1064	10128	10256	10512	101024	102048	104096	=102n+1 Each numeral is the square of the previous. This is similar to the -yllion system.

In practice, this situation does not lead to ambiguity, with the exception of Template:Zhi, which means 10¹² according to the system in common usage throughout the Chinese communities as well as in Japan and Korea, but has also been used for 10⁶ in recent years (especially in mainland China for megabyte). To avoid problems arising from the ambiguity, the PRC government never uses this character in official documents, but uses Template:Zhi) or Template:Zhi instead. Partly due to this, combinations of Template:Zhi and Template:Zhi are often used instead of the larger units of the traditional system as well, for example Template:Zhi instead of Template:Zhi. The ROC government in Taiwan uses Template:Zhi to mean 10¹² in official documents.

Large numbers from Buddhism

Template:Expand Chinese Numerals beyond Template:Zhi zǎi come from Buddhist texts in Sanskrit, but are mostly found in ancient texts. Some of the following words are still being used today, but may have transferred meanings.

Character	Pinyin	Jyutping	Tai Lo	Shanghainese	Value	Notes
Template:Zhi	Template:Transliteration	Template:Transliteration	ke̍k	Template:Transliteration	1048	Literally 'extreme'.
Template:Zhi	Template:Transliteration	Template:Transliteration	hîng-hô-sua	Template:Transliteration	1052	Literally 'sands of the Ganges', a metaphor used in a number of Buddhist texts referring to many individual grains of sand
Template:Zhi	Template:Transliteration	Template:Transliteration	a-sing-kî	a1-sen-ji	1056	From Sanskrit Template:Transliteration 'innumerable', 'infinite'
Template:Zhi	Template:Transliteration	Template:Transliteration	ná-iû-thann	Template:Transliteration	1060	From Sanskrit Template:Transliteration 'myriad'
Template:Zhi	Template:Transliteration	Template:Transliteration	put-khó-su-gī	Template:Transliteration	1064	Literally translated as "unfathomable". This word is commonly used in Chinese as a chengyu, meaning "unimaginable", instead of its original meaning of the number 1064.
Template:Zhi	Template:Transliteration	Template:Transliteration	bû-liōng tāi-siàu	Template:Transliteration	1068	Template:Zhi literally 'without measure', and can mean 1068. This word is also commonly used in Chinese as a commendatory term, means 'no upper limit'. e.g.: Template:Zhi 'a great future'. Template:Zhi 'a large number', and can mean 1072.

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.

Characters	Pinyin	Value	Notes
Template:Zhi	mò	10−12	(Ancient Chinese) Template:Zhi corresponds to the SI prefix pico-.
Template:Zhi	miǎo	10−11	(Ancient Chinese)
Template:Zhi	āi	10−10	(Ancient Chinese)
Template:Zhi	chén	10−9	Literally 'dust' Template:Zhi (S) corresponds to the SI prefix nano-.
Template:Zhi	shā	10−8	Literally, "Sand"
Template:Zhi	xiān	10−7	'fiber'
Template:Zhi	wēi	10−6	still used, corresponds to the SI prefix micro-.
Template:Zhi	hū	10−5	(Ancient Chinese)
Template:Zhi	sī	10−4	also Template:Zhi. Literally, "Thread"
Template:Zhi	háo	10−3	also Template:Zhi. still in use, corresponds to the SI prefix milli-.
Template:Zhi	lí	10−2	also Template:Zhi. still in use, corresponds to the SI prefix centi-.
Template:Zhi	fēn	10−1	still in use, corresponds to the SI prefix deci-.

Small numbers from Buddhism

Characters	Pinyin	Value	Notes
Template:Zhi	Template:Zhi	10−24	'Nirvana's tranquillity' Template:Zhi corresponds to the SI prefix yocto-.
Template:Zhi	Template:Zhi	10−23	From Sanskrit Template:Transliteration
Template:Zhi	Template:Zhi	10−22	From Sanskrit Template:Transliteration
Template:Zhi	Template:Zhi	10−21	'quiet' Template:Zhi corresponds to the SI prefix zepto-.
Template:Zhi	Template:Zhi	10−20	'void'
Template:Zhi	Template:Zhi	10−19	Literally 'six virtues'
Template:Zhi	Template:Zhi	10−18	Literally 'brevity', from Sanskrit Template:Transliteration. Template:Zhi corresponds to the SI prefix atto-.
Template:Zhi	Template:Zhi	10−17	Literally 'flick of a finger'. Still commonly used in the phrase Template:Zhi
Template:Zhi	Template:Zhi	10−16	Literally 'moment of breath'. Still commonly used in the chengyu Template:Zhi 'many things changed in a very short time'
Template:Zhi	Template:Zhi	10−15	Rarely used in modern Chinese as 'a very short time'. Template:Zhi corresponds to the SI prefix femto-.
Template:Zhi	Template:Zhi	10−14	'hesitation'
Template:Zhi	Template:Zhi	10−13	'blurred'

SI prefixes

In the People's Republic of China, the early translation for the SI prefixes in 1981 was different from those used today. The larger (Template:Zhi, Template:Zhi, Template:Zhi, Template:Zhi, Template:Zhi) and smaller Chinese numerals (Template:Zhi, Template:Zhi, Template:Zhi, Template:Zhi, Template:Zhi) were defined as translation for the SI prefixes as mega, giga, tera, peta, exa, micro, nano, pico, femto, atto, resulting in the creation of yet more values for each numeral.

The Republic of China (Taiwan) defined Template:Zhi as the translation for mega and Template:Zhi as the translation for tera. This translation is widely used in official documents, academic communities, informational industries, etc. However, the civil broadcasting industries sometimes use Template:Zhi to represent "megahertz".

Today, the governments of both China and 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
1030	Q	quetta-			Template:Zhi	kūn	Template:Zhi	kūn
1027	R	ronna-			Template:Zhi	róng	Template:Zhi	luó
1024	Y	yotta-			Template:Zhi	yáo	Template:Zhi	yòu
1021	Z	zetta-			Template:Zhi	zé	Template:Zhi	jiē
1018	E	exa-	Template:Zhi	ráng	Template:Zhi	ài	Template:Zhi	ài
1015	P	peta-	Template:Zhi	zǐ	Template:Zhi	pāi	Template:Zhi	pāi
1012	T	tera-	Template:Zhi	gāi	Template:Zhi	tài	Template:Zhi	zhào
109	G	giga-	Template:Zhi	jīng	Template:Zhi	jí	Template:Zhi	jí
106	M	mega-	Template:Zhi	zhào	Template:Zhi	zhào	Template:Zhi	bǎiwàn
103	k	kilo-	Template:Zhi	qiān	Template:Zhi	qiān	Template:Zhi	qiān
102	h	hecto-	Template:Zhi	bǎi	Template:Zhi	bǎi	Template:Zhi	bǎi
101	da	deca-	Template:Zhi	shí	Template:Zhi	shí	Template:Zhi	shí
100	(base)	one			Template:Zhi	yī	Template:Zhi	yī
10−1	d	deci-	Template:Zhi	fēn	Template:Zhi	fēn	Template:Zhi	fēn
10−2	c	centi-	Template:Zhi	lí	Template:Zhi	lí	Template:Zhi	lí
10−3	m	milli-	Template:Zhi	háo	Template:Zhi	háo	Template:Zhi	háo
10−6	μ	micro-	Template:Zhi	wēi	Template:Zhi	wēi	Template:Zhi	wēi
10−9	n	nano-	Template:Zhi	xiān	Template:Zhi	nà	Template:Zhi	nài
10−12	p	pico-	Template:Zhi	shā	Template:Zhi	pí	Template:Zhi	pí
10−15	f	femto-	Template:Zhi	chén	Template:Zhi	fēi	Template:Zhi	fēi
10−18	a	atto-	Template:Zhi	miǎo	Template:Zhi	à	Template:Zhi	à
10−21	z	zepto-			Template:Zhi	zè	Template:Zhi	jiè
10−24	y	yocto-			Template:Zhi	yāo	Template:Zhi	yōu
10−27	r	ronto-			Template:Zhi	róu	Template:Zhi	róng
10−30	q	quecto-			Template:Zhi	kuī	Template:Zhi	kuì

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 Template:Lang-zh (liǎng) is often used rather than Template:Zhi for all numbers 200 and greater with the "2" numeral (although as noted earlier this varies from dialect to dialect and person to person). Use of both Template:Zhi or Template:Zhi are acceptable for the number 200. When writing in the Cantonese dialect, Template:Zhi is used to represent the "2" numeral for all numbers. In the southern Min dialect of Chaozhou (Teochew), Template:Zhi (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]	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi
20	[2] [10] or [20]	Template:Zhi	Template:Zhi or Template:Zhi	Template:Zhi	Template:Zhi
200	[2] (èr or liǎng) [100]	Template:Zhi or Template:Zhi	Template:Zhi or Template:Zhi	Template:Zhi	Template:Zhi
2000	[2] (èr or liǎng) [1000]	Template:Zhi or Template:Zhi	Template:Zhi or Template:Zhi	Template:Zhi	Template:Zhi
45	[4] [10] [5]	Template:Zhi	Template:Zhi or Template:Zhi	Template:Zhi	Template:Zhi
2,362	[2] [1000] [3] [100] [6] [10] [2]	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi

For the numbers 11 through 19, the leading 'one' (Template:Lang-zh) 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]	Template:Zhi
12000	[1] [10000] [2] [1000]	Template:Zhi	[1] [10000] [2]	Template:Zhi or Template:Zhi
114	[1] [100] [1] [10] [4]	Template:Zhi	[1] [100] [10] [4]	Template:Zhi
1158	[1] [1000] [1] [100] [5] [10] [8]	Template:Zhi

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] (Template:Zhi).

Outside of Taiwan, digits are sometimes grouped by myriads instead of 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 × Template:Zhi = Template:Zhi. 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	Taiwan	Mainland China
12,345,678,902,345 (12,3456,7890,2345)	(12) [1,0000,0000,0000] (3456) [1,0000,0000] (7890) [1,0000] (2345)	Template:Zhi	Template:Zhi

In Taiwan, pure Arabic numerals are officially always and only grouped by thousands. Unofficially, they are often not grouped, particularly for numbers below 100,000. Mixed Arabic-Chinese numerals are often used in order to denote myriads. This is used both officially and unofficially, and come in a variety of styles:

Number	Structure	Mixed numerals
12,345,000	(1234) [1,0000] (5) [1000]	1,234萬5千
123,450,000	(1) [1,0000,0000] (2345) [1,0000]	Template:Zhi
12,345	(1) [1,0000] (2345)	Template:Zhi

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]	Template:Zhi
100,004(10,0004)	[10] [10,000] [0] [4]	Template:Zhi
10,050,026(1005,0026)	(1005) [10,000] (026) or (1005) [10,000] (26)	Template:Zhi or Template:Zhi

Fractional values

To construct a fraction, the denominator is written first, followed by Template:Zhi, then the literary possessive particle Template:Zhi, and lastly 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. For example, to express "two thirds", the structure "three parts of-this two" is used. Mixed numbers are written with the whole-number part first, followed by Template:Zhi, then the fractional part.

Fraction	Structure
2⁄3	Template:Fs interlinear
15⁄32	Template:Fs interlinear
1⁄3000	Template:Fs interlinear
3+5⁄6	Template:Fs interlinear

Percentages are constructed similarly, using Template:Zhi as the denominator. (The number 100 is typically expressed as Template:Zhi, like the English 'one hundred'. However, for percentages, Template:Zhi is used on its own.)

Percentage	Structure
25%	Template:Fs interlinear
110%	Template:Fs interlinear

Because percentages and other fractions are formulated the same, Chinese are more likely than not to express 10%, 20% etc. as 'parts of 10' (or 1⁄10, 2⁄10, etc. i.e. ; Template:Transliteration, ; Template:Transliteration, etc.) rather than "parts of 100" (or 10⁄100, 20⁄100, etc. i.e. ; Template:Transliteration, ; Template:Transliteration, etc.)

In Taiwan, the most common formation of percentages in the spoken language is the number per hundred followed by the word Template:Zhi, a contraction of the Japanese ; Template:Transliteration, itself taken from 'percent'. Thus 25% is ; Template:Transliteration.Template:Refn

Decimal numbers are constructed by first writing the whole number part, then inserting a point (Template:Zhi), and finally the fractional part. The fractional part is expressed using only the numbers for 0 to 9, similarly to English.

Decimal expression	Structure
16.98	Template:Fs interlinear
12345.6789	Template:Fs interlinear
75.4025	Template:Fs interlinear
0.1	Template:Fs interlinear

Template:Zhi functions as a number and therefore requires a measure word. For example: Template:Zhi.

Ordinal numbers

Ordinal numbers are formed by adding Template:Zhi before the number.

Ordinal	Structure
1st	Template:Fs interlinear
2nd	Template:Fs interlinear
82nd	Template:Fs interlinear

The Heavenly Stems are a traditional Chinese ordinal system.

Negative numbers

Negative numbers are formed by adding Template:Zhi before the number.

Number	Structure
−1158	Template:Fs interlinear
−3+5⁄6	Template:Fs interlinear
−75.4025	Template:Fs interlinear

Usage

Chinese grammar requires the use of classifiers (measure words) when a numeral is used together with a noun to express a quantity. For example, "three people" is expressed as Template:Lang-zh, "three (Template:Lang-zh particle) person", where Template:Lang-zh/Template:Lang-zh Template:Lang-zh is a classifier. There exist many different classifiers, for use with different sets of nouns, although Template:Lang-zh/Template:Lang-zh is the most common, and may be used informally in place of other classifiers.

Chinese uses cardinal numbers in certain situations in which English would use ordinals. For example, Template:Lang-zh (literally "three story/storey") means "third floor" ("second floor" in British Template:Section link). Likewise, Template:Lang-zh (literally "twenty-one century") is used for "21st century".

Numbers of years are commonly spoken as a sequence of digits, as in Template:Lang-zh ("two zero zero one") for the year 2001. Names of months and days (in the Western system) are also expressed using numbers: Template:Lang-zh ("one month") for January, etc.; and Template:Lang-zh ("week one") for Monday, etc. There is only one exception: Sunday is Template:Lang-zh, or informally Template:Lang-zh, both literally "week day". When meaning "week", "Template:Lang-zh" Template:Lang-zh and "Template:Lang-zh" Template:Lang-zh are interchangeable. "Template:Lang-zh" Template:Lang-zh or "Template:Lang-zh" Template:Lang-zh means "day of worship". Chinese Catholics call Sunday "Template:Lang-zh" Template:Lang-zh, "Lord's day".

Full dates are usually written in the format 2001年1月20日 for January 20, 2001 (using Template:Lang-zh "year", Template:Lang-zh "month", and Template:Lang-zh "day") – all the numbers are read as cardinals, not ordinals, with no leading zeroes, and the year is read as a sequence of digits. For brevity the Template:Lang-zh, Template:Lang-zh and Template:Lang-zh may be dropped to give a date composed of just numbers. For example "6-4" in Chinese is "six-four", short for "month six, day four" i.e. June Fourth, a common Chinese shorthand for the 1989 Tiananmen Square protests and massacre (because of the violence that occurred on June 4). For another example 67, in Chinese is sixty seven, short for year nineteen sixty seven, a common Chinese shorthand for the 1967 Hong Kong riots.

Counting rod and Suzhou numerals

File:Chounumerals.svg

Counting rod 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 (Template:Lang-zh) 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.

Hand gestures

File:Chinesische.Zahl.Sechs.jpg

Hand symbol for the number six

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 easily 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

File:Shang numerals.jpg

Shang oracle bone numerals of 14th century B.C.

File:西周金文.jpg

West Zhou dynasty bronze script

File:Rod numeral positioning.JPG

Counting rod numeral example from the Yongle Encyclopedia showing the number 71,824

File:Counting board.jpg

Japanese counting board with grids

Most Chinese numerals of later periods were descendants of the Shang dynasty oracle numerals of the 14th century BC. The oracle bone script numerals were found on tortoise shell and animal bones. In early civilizations, the Shang were able to express any numbers, however large, with only nine symbols and a counting board though it was still not positional.

Some of the bronze script numerals such as 1, 2, 3, 4, 10, 11, 12, and 13 became part of the system of rod numerals.

In this system, horizontal rod numbers are used for the tens, thousands, hundred thousands etc. It is written in Sunzi Suanjing that "one is vertical, ten is horizontal".

Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi	Template:Zhi
File:Counting rod v7.png	File:Counting rod h1.png	File:Counting rod v8.png	File:Counting rod h2.png	File:Counting rod v4.png
7	1	8	2	4

The counting rod numerals system has place value and decimal numerals for computation, and was used widely by Chinese merchants, mathematicians and astronomers from the Han dynasty to the 16th century.

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."

During the Ming and Qing dynasties (after Arabic numerals were introduced into China), some Chinese mathematicians used Chinese numeral characters as positional system digits. After the Qing period, both the Chinese numeral characters and the Suzhou numerals were replaced by Arabic numerals in mathematical writings.

Cultural influences

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

• Numbers in Chinese culture
• Celestial stem