Chinese numerals
Chinese numerals are words and characters used to denote numbers in Chinese.
Today, speakers of Chinese 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 are shared with other languages of the Chinese cultural sphere such as Japanese, Korean and Vietnamese. Most people and institutions in China and Taiwan primarily use the Arabic or mixed Arabic-Chinese systems for convenience, with traditional Chinese numerals used in finance, mainly for writing amounts on checks, banknotes, some ceremonial occasions, some boxes, and on commercials.
The other indigenous system is 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 in Chinese markets, such as those in Hong Kong before the 1990s, but have been gradually supplanted by Arabic numerals.
Characters used to represent numbers
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, 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.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, known as xiǎoxiě, and one for use in commercial or financial contexts, known as dàxiě. 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 the everyday characters to just by adding a few strokes. That would not be possible when writing using the financial characters and . They are also referred to as "banker's numerals", "anti-fraud numerals", or "banker's anti-fraud numerals". For the same reason, rod numerals were never used in commercial records.T denotes Traditional Chinese characters, while S denotes Simplified Chinese characters.
Characters with regional usage
Characters with military usage
In the People's Liberation Army of the People's Republic of China and the Republic of China Armed Forces of Taiwan, some numbers will have altered names when used for clearer radio communications. They are:- 0: renamed 洞 lit. hole
- 1: renamed 幺 lit. small
- 2: renamed 两 lit. double
- 7: renamed 拐 lit. cane, turn
- 9: renamed 勾 lit. hook
Large numbers
| Character | Factor of increase | |||||||||||
| Character | Factor of increase | |||||||||||
| Pinyin | wàn | yì | zhào | jīng | gāi | zǐ | ráng | gōu | jiàn | zhèng | zǎi | Factor of increase |
| Jyutping | maan6 | jik1 | siu6 | ging1 | goi1 | zi2 | joeng4 | kau1 | gaan3 | zing3 | zoi2 | Factor of increase |
| Hokkien POJ | bān | ek | tiāu | keng | kai | chí | jiông | ko͘ | kàn | chèng | cháiⁿ | Factor of increase |
| Alternative | / | |||||||||||
| Rank | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | =n |
| "short scale" | 104 | 105 | 106 | 107 | 108 | 109 | 1010 | 1011 | 1012 | 1013 | 1014 | =10n+3 Each numeral is 10 times the previous. |
| "myriad scale" | 104 | 108 | 1012 | 1016 | 1020 | 1024 | 1028 | 1032 | 1036 | 1040 | 1044 | =104n Each numeral is 10,000 or 万 times the previous. |
| "mid-scale" | 104 | 108 | 1016 | 1024 | 1032 | 1040 | 1048 | 1056 | 1064 | 1072 | 1080 | =108 Starting with 亿, each numeral is 108 or 万乘以万 times the previous. |
| "long scale" | 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 兆, 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. To avoid problems arising from the ambiguity, the PRC government never uses this character in official documents, but uses 万亿 or 太 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 instead of 京. The ROC government in Taiwan uses 兆 to mean 1012 in official documents.
Large numbers from Buddhism
Numerals beyond 載 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.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.Small numbers from Buddhism
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 and smaller Chinese numerals 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 defined 百萬 as the translation for mega and 兆 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 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.
Reading and transcribing numbers
Whole numbers
Multiple-digit numbers are constructed using a multiplicative principle; first the digit itself, then the place ; then the next digit.In Mandarin, the multiplier is often used rather than for all numbers 200 and greater with the "2" numeral. Use of both 兩 or 二 are acceptable for the number 200. When writing in the Cantonese dialect, 二 is used to represent the "2" numeral for all numbers. In the southern Min dialect of Chaozhou, 兩 is used to represent the "2" numeral in all numbers from 200 onwards. Thus:
For the numbers 11 through 19, the leading "one" 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:
Notes:
- Nothing is ever omitted in large and more complicated numbers such as this.
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 × = . If one of the numbers is between 10 and 19, the leading "one" is omitted as per the above point. Hence :
| Number | Structure | Taiwan | Mainland China |
| 12,345,678,902,345 | 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. 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 | 1,234萬5千 | |
| 123,450,000 | 1億2345萬 | |
| 12,345 | 1萬2345 |
Interior zeroes before the unit position must be spelt explicitly. The reason for this is that trailing zeroes 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 | 二百零五 | |
| 100,004 | 十萬零四 | |
| 10,050,026 | or | 一千零五萬零二十六 or 一千零五萬二十六 |
Fractional values
To construct a fraction, the usual morphosyntax of the language is used door of. Hence to express e.g. "2 parts of 3", the structure "of 3 parts 2" is used — the denominator is written first, followed by, then the particle ; 'of this'/-'s 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. Mixed numbers are written with the whole-number part first, followed by, then the fractional part.| Fraction | Structure | Characters | Pinyin |
| 2/3 | |||
| 15/32 | ' | ||
| 1/3000 | ' | ||
| 3 5/6 |
Percentages are constructed similarly, using as the denominator. The before is omitted.
| Percentage | Structure | Characters | Pinyin |
| 25% | |||
| 110% |
Because percentages and other fractions are formulated the same, Chinese are more likely than not to express 10%, 20% etc. as "parts of 10" rather than "parts of 100"
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 wikt:パーセント; pāsento, itself taken from the English "percent". Thus 25% is 二十五趴; èrshí wǔ pā.
Decimal numbers are constructed by first writing the whole number part, then inserting a 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 | ||
| 12345.6789 | ||
| 75.4025 | or | |
| 0.1 |
, functions as a number and therefore requires a measure word. Example: is "half a glass of water".
Ordinal numbers
Ordinal numbers are formed by adding before the number.| Ordinal | Structure | Characters | Pinyin |
| 1st | dì-yī | ||
| 2nd | dì-èr | ||
| 82nd | dì-bāshí-èr |
The Heavenly Stems are a traditional Chinese ordinal system.
Negative numbers
Negative numbers are formed by adding fù before the number.| Number | Structure | Characters |
| −1158 | ||
| −3 5/6 | ||
| −75.4025 |
Usage
requires the use of classifiers when a numeral is used together with a noun to express a quantity. For example, "three people" is expressed as , "three person", where / ' is a classifier. There exist many different classifiers, for use with different sets of nouns, although / 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, means "third floor". Likewise, is used for "21st century".
Numbers of years are commonly spoken as a sequence of digits, as in for the year 2001. Names of months and days are also expressed using numbers: for January, etc.; and for Monday, etc. Only one exception, Sunday is, or informally, both literally "week day". When meaning "week", "" and "" are interchangeable. "" or "" means "day of worship". Chinese Catholics call Sunday "" ', "Lord's day".
Full dates are usually written in the format 2001年1月20日 for January 20, 2001 – 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, and 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. For another example 67, in Chinese is sixty seven, short for year nineteen sixty seven, a common Chinese shorthand for the Hong Kong 1967 leftist riots.
Counting rod and Suzhou numerals
In the same way that Roman numerals were standard in ancient and medieval Europe for mathematics and commerce, the Chinese formerly used the rod numerals, which is a positional system. The Suzhou numerals 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
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.Historical use of numerals in China
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.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's written in Sunzi Suanjing that "one is vertical, ten is horizontal".
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.
In 690 AD, Empress Wǔ promulgated Zetian characters, one of which was "〇". The word is now used as a synonym for the number zero.
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 , 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, 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.