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Chinese numerals are words and characters used to denotenumbers inwritten Chinese.
Today, speakers of Chinese languages use three writtennumeral systems: the system ofArabic numerals used worldwide, and two indigenous systems. The more familiar indigenous system is based onChinese characters that correspond tonumerals in the spoken language. These may be shared with other languages of theChinese cultural sphere such asKorean,Japanese, andVietnamese. 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.[citation needed]
The other indigenous system consists of theSuzhou numerals, orhuama, a positional system, the only surviving form of therod numerals. These were once used by Chinese mathematicians, and later by merchants in Chinese markets, such as those inHong Kong until the 1990s, but were gradually supplanted by Arabic numerals.
The Chinese character numeral system consists of theChinese characters used by theChinese 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 systemper se. Since it reflects spoken language, it does not use the positional system as inArabic numerals, in the same way that spelling out numbers in English does not.
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 asxiǎoxiě (小寫;小写; 'small writing'), and one for use in commercial, accounting or financial contexts, known asdàxiě (大寫;大写; 'big writing' or 'capital numbers'). The latter were developed byWu Zetian (fl. 690–705) and were further refined by theHongwu Emperor (fl. 1328–1398).[1] 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.[2] A forger could easily change the everyday characters三十 (30) to五千 (5000) just by adding a few strokes. That would not be possible when writing using the financial characters參拾 (30) and伍仟 (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 | Simplified[3]: §52 | Traditional | Simplified | ||||||
| 0 | 零 | 零 or〇 | líng | ling4 | khòng, lîng | 6lin | Usually零 is preferred, but in some areas, 〇 may be a more common informal way to represent zero. The original Chinese character is空 or〇,零 is referred as remainder something less than 1 yet not nil [說文] referred. The traditional零 is more often used in schools. In Unicode, 〇 is treated as aChinese symbol or punctuation, rather than aChinese ideograph. | ||
| 1 | 壹 | 一 | yī | jat1 | it, tsi̍t | 7iq | Also弌 (obsolete financial[dubious –discuss]), can be easily manipulated into弍; 'two' or弎; 'three'. | ||
| 2 | 貳 | 贰 | 二 | èr | ji6 | jī, nn̄g | 6gni,6er,6lian | Also弍 (obsolete, financial[dubious –discuss]), can be easily manipulated into弌; 'one' or弎; 'three'. Also两;兩. | |
| 3 | 參 | 叁 | 三 | sān | saam1 | sam, sann | 1se | Also弎 (obsolete financial[dubious –discuss]), which can be easily manipulated into弌; 'one' or弍; 'two'. | |
| 4 | 肆 | 四 | sì | sei3 | sù, sì | 5sy | Also䦉 (obsolete financial).[nb 1] | ||
| 5 | 伍 | 五 | wǔ | ng5 | ngóo, gōo | 6ng | — | ||
| 6 | 陸 | 陆 | 六 | liù | luk6 | liok, la̍k | 8loq | — | |
| 7 | 柒 | 七 | qī | cat1 | tshit | 7chiq | — | ||
| 8 | 捌 | 八 | bā | baat3 | pat, peh | 7paq | — | ||
| 9 | 玖 | 九 | jiǔ | gau2 | kiú, káu | 5cieu | — | ||
| 10 | 拾 | 十 | shí | sap6 | si̍p, tsa̍p | 8zeq | Although some people use什 as financial[citation needed], it is not ideal because it can be easily manipulated into伍; 'five' or仟; 'thousand'. | ||
| 100 | 佰 | 百 | bǎi | baak3 | pek, pah | 7paq | — | ||
| 1,000 | 仟 | 千 | qiān | cin1 | tshian, tshing | 1chi | — | ||
| 104 | 萬 | 万 | 萬 | 万 | wàn | maan6 | bān | 6ve | Chinese numbers group by ten-thousands; seeReading and transcribing numbers below. |
| 108 | 億 | 亿 | 億 | 亿 | yì | jik1 | ik | 5i,6yi | For variant meanings and words for higher values, seeLarge 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.
| Financial | Normal | Value | Pinyin | Standard alternative | Notes |
|---|---|---|---|---|---|
| 空 | 0 | kòng | 零 | Historically, the use of空 for 'zero' predates零. This is now archaic in mostvarieties of Chinese, but it is still used in most ofSouthern Min. | |
| 洞 | 0 | dòng | 零 | Literally 'a hole', is analogous to the shape of⟨0⟩ and⟨〇⟩, it is used to unambiguously pronounce#0 inradio communication.[4][5] | |
| 幺 | 1 | yāo | 一 | Literally 'the smallest', it is used to unambiguously pronounce#1 in radio communication.[4][5] This usage is not observed in Cantonese except for十三幺, which refers to a special winning hand inmahjong. | |
| 蜀 | 1 | shǔ | 一 | In mostMin varieties, there are two words meaning 'one'. For example, inHokkien,chi̍t is used before aclassifier: 'one person' ischi̍t ê lâng, notit ê lâng. Inwritten Hokkien,一 is often used for bothchi̍t andit, but some authors differentiate, writing蜀 forchi̍t and一 forit. | |
| 两;兩 | 2 | liǎng | 二 | Used instead of二 before aclassifier. For example, 'two people' is两个人, not二个人. However, in some lects such as Shanghainese,兩 is the generic term used for two in most contexts, such as四十兩 and not四十二. It appears where 'a pair of' might in English, but两 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. It is used to unambiguously pronounce#2 in radio communication.[4][5] | |
| 俩;倆 | 2 | liǎ | 兩 | In regional dialects ofNortheastern Mandarin,倆 represents a "lazy" pronunciation of兩 within the local dialect. It can be used as an alternative for兩个; 'two of', e.g.我们倆;wǒmen liǎ; 'the two of us', as opposed to我们兩个;wǒmen liǎng gè. A measure word never follows倆. | |
| 仨 | 3 | sā | 三 | In regional dialects ofNortheastern Mandarin,仨 represents a "lazy" pronunciation of three within the local dialect. It can be used as a general number to represent 'three', e.g.第仨号;dìsāhào; 'number three';星期仨;xīngqīsā; 'Wednesday', or as an alternative for三个; 'three of', e.g.我们仨;wǒmen sā; 'the three of us', as opposed to我们三个;wǒmen sān gè). Regardless of usage, a measure word never follows仨. | |
| 拐 | 7 | guǎi | 七 | Literally 'a turn' or 'a walking stick' and is analogous to the shape of⟨7⟩ and七, it is used to unambiguously pronounce#7 in radio communication.[4][5] | |
| 勾 | 9 | gōu | 九 | Literally 'a hook' and is analogous to the shape of⟨9⟩, it is used to unambiguously pronounce#9 in radio communication.[4][5] | |
| 呀 | 10 | yà | 十 | In spokenCantonese,呀 (aa6) can be used in place of十 when it is used in the middle of a number, preceded by a multiplier and followed by a ones digit, e.g.六呀三 '63', it is not used by itself to mean 10. This usage is not observed in Mandarin. | |
| 念 | 廿 | 20 | niàn | 二十 | A contraction of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. SeeReading and transcribing numbers section below. In spokenCantonese,廿 (jaa6) can be used in place of二十 when followed by another digit such as in numbers 21–29 (e.g.廿三 '23', a measure word, e.g.廿個, a noun, or in a phrase like廿幾 'twenty-something'. It is not used by itself to mean 20.廿;jiāp/gnie6 is still used in place of二十 in Southern Min and Wu.卄 is a rare variant. |
| 卅 | 30 | sà | 三十 | A contraction of三十. The written form is still used to abbreviate date references in Chinese. For example,May 30 Movement (五卅運動). The spoken form is still used in various dialects of Chinese. In spokenCantonese,卅;saa1 can be used in place of三十 when followed by another digit such as in numbers 31–39, a measure word (e.g.卅個), a noun, or in phrases like卅幾 'thirty-something'. It is not used by itself to mean 30. When spoken卅 is pronounced as卅呀;saa1-aa6. Thus卅一 '31', is pronounced assaa1-aa6-jat1. | |
| 卌 | 40 | xì | 四十 | A contraction of四十. Found in historical writings written inLiterary Chinese. Spoken form is still used in various dialects of Chinese, albeit very rare. SeeReading and transcribing numbers section below. In spoken Cantonese卌;sei3 can be used in place of四十 when followed by another digit such as in numbers 41–49, a measure word (e.g.卌個), a noun, or in phrases like卌幾 'forty-something', it is not used by itself to mean 40. When spoken,卌 is pronounced as卌呀;sei3-aa6. Thus卌一;41, is pronounced assei3-aa6-jat1. Similarly, in Southern Min 41 can be referred to as卌一;siap it. | |
| 皕 | 200 | bì | 二百 | Very rarely used; one example is in the name of a library inHuzhou,皕宋樓;Bìsòng Lóu. |
For numbers larger than 10,000, similarly to thelong 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 theYellow Emperor in the 6th century book by Zhen Luan,Wujing suanshu; 'Arithmetic in Five Classics'. In modern Chinese, only the second system is used, in which the same ancient names are used, but each represents amyriad,萬;wàn times the previous:
| Character | 萬 | 億 | 兆 | 京 | 垓 | 秭 | 穰 | 溝 | 澗 | 正 | 載 | Factor of increase |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Character (S) | 万 | 亿 | 沟 | 涧 | 载 | |||||||
| Pinyin | wàn | yì | zhào | jīng | gāi | zǐ | rǎng | gōu | jiàn | zhèng | zǎi | |
| Jyutping | maan6 | jik1 | siu6 | ging1 | goi1 | zi2 | joeng5 | kau1 | gaan3 | zing3 | zoi2 | |
| Tai Lo | bān | ik | tiāu | king | kai | cí | jiông | koo | kàn | cèng | cáinn | |
| Wugniu | 6ve | 6yi | 6zau | 1cin | 1ke | 3tsy | 4gnian | 1keu | 5ke | 5tsen | 5tse | |
| Alternative | 经;經 | 𥝱 | 壤 | |||||||||
| Rank | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | =n |
| "short scale" (下數) | 104 | 105 | 106 | 107 | 108 | 109 | 1010 | 1011 | 1012 | 1013 | 1014 | =10n+3 Each numeral is 10 (十;shí) times the previous. |
| "myriad scale" (萬進, current usage) | 104 | 108 | 1012 | 1016 | 1020 | 1024 | 1028 | 1032 | 1036 | 1040 | 1044 | =104n Each numeral is 10,000 (万;萬;wàn) times the previous. |
| "mid-scale" (中數) | 104 | 108 | 1016 | 1024 | 1032 | 1040 | 1048 | 1056 | 1064 | 1072 | 1080 | =108(n-1) Starting with亿, each numeral is 108 (万乘以万;萬乘以萬;wàn chéngyǐ wàn; '10000 times 10000') times the previous. |
| "long scale" (上數) | 104 | 108 | 1016 | 1032 | 1064 | 10128 | 10256 | 10512 | 101024 | 102048 | 104096 | =102n+1 Each numeral is thesquare of the previous. This is similar to the-yllion system. |
In practice, this situation does not lead to ambiguity, with the exception of兆;zhào, which means 1012 according to the system in common usage throughout the Chinese communities as well as inJapan andKorea, but has also been used for 106 in recent years (especially in mainland China formegabyte). To avoid problems arising from the ambiguity, thePRC government never uses this character in official documents, but uses万亿;wànyì) or太;tài; 'tera-' instead. Partly due to this, combinations of万 and亿 are often used instead of the larger units of the traditional system as well, for example亿亿;yìyì instead of京. TheROC government inTaiwan uses兆;zhào to mean 1012 in official documents.
 | You can helpexpand this article with text translated fromthe corresponding article in Chinese. (September 2010)Click [show] for important translation instructions.
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Numerals beyond載 zǎi come fromBuddhist texts inSanskrit, 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 |
|---|---|---|---|---|---|---|
| 极;極 | jí | gik6 | ke̍k | jiq8 | 1048 | Literally 'extreme'. |
| 恒河沙;恆河沙 | héng hé shā | hang4 ho4 saa1 | hîng-hô-sua | ghen2-wu-so | 1052[citation needed] | Literally 'sands of theGanges', a metaphor used in a number ofBuddhist texts referring to many individual grains of sand |
| 阿僧祇 | ā sēng qí | aa1 zang1 kei4 | a-sing-kî | a1-sen-ji | 1056 | From SanskritAsaṃkhyeyaअसंख्येय 'innumerable', 'infinite' |
| 那由他 | nà yóu tā | naa5 jau4 taa1 | ná-iû-thann | na1-yeu-tha | 1060 | From Sanskritnayutaनियुत 'myriad' |
| 不可思議;不可思议 | bùkě sīyì | bat1 ho2 si1 ji3 | put-khó-su-gī | peq7-khu sy1-gni | 1064 | Literally translated as "unfathomable". This word is commonly used in Chinese as achengyu, meaning "unimaginable", instead of its original meaning of the number 1064. |
| 无量大数;無量大數 | wú liàng dà shù | mou4 loeng6 daai6 sou3 | bû-liōng tāi-siàu | m6-lian du6-su | 1068 | 无量 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.:前途无量 'a great future'.大数 'a large number', and can mean 1072. |
The following are characters used to denote smallorder 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 |
|---|---|---|---|
| 漠 | mò | 10−12 | (Ancient Chinese) |
| 渺 | miǎo | 10−11 | (Ancient Chinese) |
| 埃 | āi | 10−10 | (Ancient Chinese) |
| 尘;塵 | chén | 10−9 | Literally 'dust' 纳;奈 (S) corresponds to the SI prefixnano-. |
| 沙 | shā | 10−8 | Literally, "Sand" |
| 纤;纖 | xiān | 10−7 | 'fiber' |
| 微 | wēi | 10−6 | still used, corresponds to the SI prefixmicro-. |
| 忽 | hū | 10−5 | (Ancient Chinese) |
| 丝;絲 | sī | 10−4 | also秒. Literally, "Thread" |
| 毫 | háo | 10−3 | also毛. still in use, corresponds to the SI prefixmilli-. |
| 厘 | lí | 10−2 | also釐. still in use, corresponds to the SI prefixcenti-. |
| 分 | fēn | 10−1 | still in use, corresponds to the SI prefixdeci-. |
| Characters | Pinyin | Value | Notes |
|---|---|---|---|
| 涅槃寂静;涅槃寂靜 | niè pán jì jìng | 10−24 | 'Nirvana's tranquillity' |
| 阿摩罗;阿摩羅 | ā mó luó | 10−23 | From Sanskritअमलamala |
| 阿赖耶;阿頼耶 | ā lài yē | 10−22 | From Sanskritआलयālaya |
| 清静;清靜 | qīng jìng | 10−21 | 'quiet' 仄;介 corresponds to the SI prefixzepto-. |
| 虚空;虛空 | xū kōng | 10−20 | 'void' |
| 六德 | liù dé | 10−19 | Literally 'six virtues' |
| 刹那;剎那 | chà nà | 10−18 | Literally 'brevity', from Sanskritक्षणksaṇa.阿 corresponds to the SI prefixatto-. |
| 弹指;彈指 | tán zhǐ | 10−17 | Literally 'flick of a finger'. Still commonly used in the phrase弹指一瞬间; 'a very short time' |
| 瞬息 | shùn xī | 10−16 | Literally 'moment of breath'. Still commonly used in thechengyu瞬息万变 'many things changed in a very short time' |
| 须臾;須臾 | xū yú | 10−15 | Rarely used in modern Chinese as 'a very short time'.飞;飛 corresponds to the SI prefixfemto-. |
| 逡巡 | qūn xún | 10−14 | 'hesitation' |
| 模糊 | mó hu | 10−13 | 'blurred' |
In the People's Republic of China, the early translation for theSI prefixes in 1981 was different from those used today. The larger (兆,京,垓,秭,穰) and smaller Chinese numerals (微,纖,沙,塵,渺) were defined as translation for the SI prefixes asmega,giga,tera,peta,exa,micro,nano,pico,femto,atto, resulting in the creation of yet more values for each numeral.[6]
The Republic of China (Taiwan) defined百萬 as the translation formega and兆 as the translation fortera. 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, 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.
| Value | Symbol | English | Early translation | PRC standard | ROC standard[7] | |||
|---|---|---|---|---|---|---|---|---|
| 1030 | Q | quetta- | 昆 | kūn | 昆 | kūn | ||
| 1027 | R | ronna- | 容 | róng | 羅 | luó | ||
| 1024 | Y | yotta- | 尧 | yáo | 佑 | yòu | ||
| 1021 | Z | zetta- | 泽 | zé | 皆 | jiē | ||
| 1018 | E | exa- | 穰[6] | ráng | 艾 | ài | 艾 | ài |
| 1015 | P | peta- | 秭[6] | zǐ | 拍 | pāi | 拍 | pāi |
| 1012 | T | tera- | 垓[6] | gāi | 太 | tài | 兆 | zhào |
| 109 | G | giga- | 京[6] | jīng | 吉 | jí | 吉 | jí |
| 106 | M | mega- | 兆[6] | 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 | (base) | one | 一 | yī | 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[6] | wēi | 微 | wēi | 微 | wēi |
| 10−9 | n | nano- | 纖[6] | xiān | 纳 | nà | 奈 | nài |
| 10−12 | p | pico- | 沙[6] | shā | 皮 | pí | 皮 | pí |
| 10−15 | f | femto- | 塵[6] | chén | 飞 | fēi | 飛 | fēi |
| 10−18 | a | atto- | 渺[6] | miǎo | 阿 | à | 阿 | à |
| 10−21 | z | zepto- | 仄 | zè | 介 | jiè | ||
| 10−24 | y | yocto- | 幺 | yāo | 攸 | yōu | ||
| 10−27 | r | ronto- | 柔 | róu | 絨 | róng | ||
| 10−30 | q | quecto- | 亏 | kuī | 匱 | kuì | ||
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 200 and greater 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 thesouthern 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] (èr or 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] [1000] [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;yī) 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] | 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 | ||
Notes:
In certain older texts like the Protestant Bible, or in poetic usage, numbers such as 114 may bewritten as [100] [10] [4] (百十四).
Outside of Taiwan, digits are sometimes grouped bymyriads 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 ×萬;wàn =億;yì. 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) | 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 | 十二兆三千四百五十六亿七千八百九十万二千三百四十五 |
In Taiwan, pure Arabic numerals are officially always and only grouped by thousands.[8] 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[9] |
| 123,450,000 | (1) [1,0000,0000] (2345) [1,0000] | 1億2345萬[10] |
| 12,345 | (1) [1,0000] (2345) | 1萬2345[11] |
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] (026) or (1005) [10,000] (26) | 一千零五萬零二十六 or一千零五萬二十六 |
To construct a fraction, thedenominator is written first, followed by分;fēn; 'part', then the literary possessive particle之;zhī; 'of this', and lastly thenumerator. 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又;yòu; 'and', then the fractional part.
| Fraction | Structure |
|---|---|
| 2⁄3 | 三 sān 3 分 fēn parts 之 zhī of this 二 èr 2 三分之二 sān fēn zhī èr 3 parts {of this} 2 |
| 15⁄32 | 三 sān 3 十 shí 10 二 èr 2 分 fēn parts 之 zhī of this 十 shí 10 五 wǔ 5 三十二分之十五 sān shí èr fēn zhī shí wǔ 3 10 2 parts {of this} 10 5 |
| 1⁄3000 | 三 sān 3 千 qiān 1000 分 fēn parts 之 zhī of this 一 yī 1 三千分之一 sān qiān fēn zhī yī 3 1000 parts {of this} 1 |
| 3+5⁄6 | 三 sān 3 又 yòu and 六 liù 6 分 fēn parts 之 zhī of this 五 wǔ 5 三又六分之五 sān yòu liù fēn zhī wǔ 3 and 6 parts {of this} 5 |
Percentages are constructed similarly, using百;bǎi; '100' as the denominator. (The number 100 is typically expressed as一百;yībǎi; 'one hundred', like the English 'one hundred'. However, for percentages,百 is used on its own.)
| Percentage | Structure |
|---|---|
| 25% | 百 bǎi 100 分 fēn parts 之 zhī of this 二 èr 2 十 shí 10 五 wǔ 5 百分之二十五 bǎi fēn zhī èr shí wǔ 100 parts {of this} 2 10 5 |
| 110% | 百 bǎi 100 分 fēn parts 之 zhī of this 一 yī 1 百 bǎi 100 一 yī 1 十 shí 10 百分之一百一十 bǎi fēn zhī yī bǎi yī shí 100 parts {of this} 1 100 1 10 |
Because percentages and other fractions are formulated the same, Chinese are more likely than not to express 10%, 20% etc. as 'parts of 10' (or1⁄10,2⁄10, etc. i.e.十分之一;shí fēnzhī yī,十分之二;shí fēnzhī èr, etc.) rather than "parts of 100" (or10⁄100,20⁄100, etc. i.e.百分之十;bǎi fēnzhī shí,百分之二十;bǎi fēnzhī èrshí, etc.)
In Taiwan, the most common formation of percentages in the spoken language is the number per hundred followed by the word趴;pā, a contraction of the Japaneseパーセント;pāsento, itself taken from 'percent'. Thus 25% is二十五趴;èrshíwǔ pā.[nb 2]
Decimal numbers are constructed by first writing the whole number part, then inserting a point (点;點;diǎn), 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 | 十 shí 10 六 liù 6 點 diǎn point 九 jiǔ 9 八 bā 8 十六點九八 shí liù diǎn jiǔ bā 10 6 point 9 8 |
| 12345.6789 | 一 yī 1 萬 wàn 10000 兩 liǎng 2 千 qiān 1000 三 sān 3 百 bǎi 100 四 sì 4 十 shí 10 五 wǔ 5 點 diǎn point 六 liù 6 七 qī 7 八 bā 8 九 jiǔ 9 一萬兩千三百四十五點六七八九 yī wàn liǎng qiān sān bǎi sì shí wǔ diǎn liù qī bā jiǔ 1 10000 2 1000 3 100 4 10 5 point 6 7 8 9 |
| 75.4025 | 七 七 qī 7 十 十 shí 10 五 五 wǔ 5 點 點 diǎn point 四 四 sì 4 〇 零 líng 0 二 二 èr 2 五 五 wǔ 5 七十五點四〇二五 七十五點四零二五 qī shí wǔ diǎn sì líng èr wǔ 7 10 5 point 4 0 2 5 |
| 0.1 | 零 líng 0 點 diǎn point 一 yī 1 零點一 líng diǎn yī 0 point 1 |
半;bàn; 'half' functions as a number and therefore requires ameasure word. For example:半杯水;bàn bēi shuǐ; 'half a glass of water'.
Ordinal numbers are formed by adding第;dì; 'sequence' before the number.
| Ordinal | Structure |
|---|---|
| 1st | 第 dì sequence 一 yī 1 第 一 dì yī sequence 1 |
| 2nd | 第 dì sequence 二 èr 2 第 二 dì èr sequence 2 |
| 82nd | 第 dì sequence 八 bā 8 十 shí 10 二 èr 2 第八十 二 dì bā shí èr sequence 8 10 2 |
TheHeavenly Stems are a traditional Chinese ordinal system.
Negative numbers are formed by adding负;負;fù before the number.
| Number | Structure |
|---|---|
| −1158 | 負 fù negative 一 yī 1 千 qiān 1000 一 yī 1 百 bǎi 100 五 wǔ 5 十 shí 10 八 bā 8 負一千一百五十 八 fù yī qiān yī bǎi wǔ shí bā negative 1 1000 1 100 5 10 8 |
| −3+5⁄6 | 負 fù negative 三 sān 3 又 yòu and 六 liù 6 分 fēn parts 之 zhī of this 五 wǔ 5 負三又六分之 五 fù sān yòu liù fēn zhī wǔ negative 3 and 6 parts {of this} 5 |
| −75.4025 | 負 fù negative 七 qī 7 十 shí 10 五 wǔ 5 點 diǎn point 四 sì 4 零 líng 0 二 èr 2 五 wǔ 5 負七十五點四零二 五 fù qī shí wǔ diǎn sì líng èr wǔ negative 7 10 5 point 4 0 2 5 |
Chinese grammar requires the use ofclassifiers (measure words) when a numeral is used together with a noun to express a quantity. For example, "three people" is expressed as三个人;三個人;sān ge rén, "three (ge particle) person", where个/個ge is aclassifier. There exist manydifferent classifiers, for use with different sets of nouns, although个/個 is the most common, and may be used informally in place of other classifiers.
Chinese usescardinal numbers in certain situations in which English would useordinals. For example,三楼/三樓;sān lóu (literally "threestory/storey") means "third floor" ("second floor" in British§ Numbering). Likewise,二十一世纪/二十一世紀;èrshí yī shìjì (literally "twenty-one century") is used for "21st century".[12]
Numbers of years are commonly spoken as a sequence of digits, as in二零零一;èr líng líng yī ("two zero zero one") for the year 2001.[13] Names of months and days (in the Western system) are also expressed using numbers:一月;yīyuè ("one month") for January, etc.; and星期一;xīngqīyī ("week one") for Monday, etc. There is only one exception: Sunday is星期日;xīngqīrì, or informally星期天;xīngqītiān, both literally "week day". When meaning "week", "星期"xīngqī and "禮拜;礼拜"lǐbài are interchangeable. "禮拜天"lǐbàitiān or "禮拜日"lǐbàirì means "day of worship".Chinese Catholics call Sunday "主日"zhǔrì, "Lord's day".[14]
Full dates are usually written in the format 2001年1月20日 for January 20, 2001 (using年;nián "year",月;yuè "month", and日;rì "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 thenián,yuè andrì 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 the1989 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 the1967 Hong Kong riots.
In the same way thatRoman numerals were standard in ancient and medieval Europe for mathematics and commerce, the Chinese formerly used therod 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 theSouthern Song rod numerals. Nowadays, thehuāmǎ system is only used for displaying prices in Chinese markets or on traditional handwritten invoices.
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.
Most Chinese numerals of later periods were descendants of theShang dynasty oracle numerals of the 14th century BC. Theoracle 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.[16]
Some of the bronze script numerals such as 1, 2, 3, 4, 10, 11, 12, and 13 became part of the system ofrod numerals.
In this system, horizontal rod numbers are used for the tens, thousands, hundred thousands etc. It is written inSunzi Suanjing that "one is vertical, ten is horizontal".[17]
| 七 | 一 | 八 | 二 | 四 |
|---|---|---|---|---|
 |  |  |  |  |
| 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 theHan 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."[18]
During theMing andQing 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.
Traditional Chinese numeric characters are also used inJapan andKorea and were used inVietnam 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.
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