Chinese numerals
Chinese numerals are words and characters used to denote numbers in written Chinese. Speakers of Chinese languages use three written numeral systems: the international system of Arabic numerals, 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
Traditionally, the Chinese numeral system is a sign-value notation consisting of the same Chinese characters used by the Chinese written language to write spoken numbers. Similar to spelling-out numbers in English, it is not an independent system per se. Since it reflects spoken language, it generally does not use the positional system as in Arabic numerals, in the same way that spelling out numbers in English does not. In modern times, Chinese numerals may adopt a positional system in some contexts, though this is uncommon.Ordinary numerals
There are characters representing the numbers zero through nine, and other characters representing powers of ten such as tens, hundreds, thousands, ten thousands and hundred millions. There are two sets of characters for ordinary Chinese numerals: one for everyday writing, known as , and another for use in commercial, accounting or financial contexts, known as .Financial numerals
The financial numerals were developed by Wu Zetian and were further refined by the Hongwu Emperor. They were adopted because the characters used for writing everyday 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 characters to 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" or "anti-fraud numerals". For the same reason, rod numerals were never used in commercial records. Outside China, the financial numerals were adopted in Korea and in Japan for similar purposes.- Wugniu is a pan-Wu romanization scheme, but the exact romanization depends on the variety. The romanization listed here is specifically for Shanghainese.
Regional, contextual, and historic variation
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,. In modern Chinese, only the second system is used, in which the same ancient names are used, but each represents a myriad, times the previous:| Character | Factor of increase | |||||||||||
| Character | Factor of increase | |||||||||||
| Pinyin | Factor of increase | |||||||||||
| Jyutping | Factor of increase | |||||||||||
| Tai Lo | Factor of increase | |||||||||||
| Wugniu | 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 times the previous. |
| "mid-scale" | 104 | 108 | 1016 | 1024 | 1032 | 1040 | 1048 | 1056 | 1064 | 1072 | 1080 | =108 Starting with, each numeral is 108 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, which means 1012 according to the system in common usage throughout Chinese communities as well as in Japan and Korea, but has also been used for 106 in recent years. To avoid ambiguity, the PRC government never uses this character in official documents, but uses or instead. Partly due to this, combinations of and are often used instead of the larger units of the traditional system as well, for example instead of. The ROC government in Taiwan uses to mean 1012 in official documents.
Large numbers from Buddhism
Numerals beyond 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 |
| ke̍k | 1048 | Literally 'extreme'. | ||||
| hîng-hô-sua | 1052 | Literally 'sands of the Ganges', a metaphor used in a number of Buddhist texts referring to many individual grains of sand | ||||
| a-sing-kî | a1-sen-ji | 1056 | From Sanskrit असंख्येय 'innumerable', 'infinite' | |||
| ná-iû-thann | 1060 | From Sanskrit नियुत 'myriad' | ||||
| put-khó-su-gī | 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. | ||||
| bû-liōng tāi-siàu | 1068 | 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.: 'a great future'. '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 |
| mò | 10−12 | corresponds to the SI prefix pico-. | |
| miǎo | 10−11 | ||
| āi | 10−10 | ||
| chén | 10−9 | Literally 'dust' corresponds to the SI prefix nano-. | |
| shā | 10−8 | Literally, "Sand" | |
| xiān | 10−7 | 'fiber' | |
| wēi | 10−6 | still used, corresponds to the SI prefix micro-. | |
| hū | 10−5 | ||
| sī | 10−4 | also. Literally, "Thread" | |
| háo | 10−3 | also. still in use, corresponds to the SI prefix milli-. | |
| lí | 10−2 | also. still in use, corresponds to the SI prefix centi-. | |
| fēn | 10−1 | still in use, corresponds to the SI prefix deci-. |
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 as the translation for mega and 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 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, 兩 rather than is often used for all numbers 200 and greater to represent the "2" numeral. Use of both or are acceptable for the number 200. When writing in the Cantonese dialect, is used to represent the "2" numeral for all numbers. In the southern Min dialect of Chaozhou, 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:
In certain older texts like the Protestant Bible, or in poetic usage, numbers such as 114 may be written as .
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 |
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 | ||
| 12,345 |
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 | ||
| 100,004 | ||
| 10,050,026 | or | or |
Fractional values
To construct a fraction, the denominator is written first, followed by, then the literary possessive particle, and lastly the numerator. 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, then the fractional part.| Fraction | Structure |
Percentages are constructed similarly, using as the denominator.
| Percentage | Structure |
| 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, a contraction of the Japanese パーセント;, itself taken from 'percent'. Thus 25% is 二十五趴;.
Decimal numbers are constructed by first writing the whole number part, then inserting a point, 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 | |
| 12345.6789 | |
| 75.4025 | |
| 0.1 |
functions as a number and therefore requires a measure word. For example:.
Ordinal numbers
Ordinal numbers are formed by adding before the number.| Ordinal | Structure |
| 1st | |
| 2nd | |
| 82nd |
The Heavenly Stems are a traditional Chinese ordinal system.
Negative numbers
Negative numbers are formed by adding before the number.| Number | Structure |
| −1158 | |
| −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 s=三, "three person", where s=个/labels=no s= is a classifier. There exist many different classifiers, for use with different sets of nouns, although s=个/labels=no 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, s= means "third floor". Likewise, labels=no is used for "21st century".
Numbers of years are commonly spoken as a sequence of digits, as in labels=no for the year 2001. Names of months and days are also expressed using numbers: labels=no for January, etc.; and labels=no for Monday, etc. There is only one exception: Sunday is labels=no, or informally labels=no, both literally "week day". When meaning "week", "c=星期" s= and "c=" s= are interchangeable. "c=禮拜天" s= or "c=禮拜日" s= means "day of worship". Chinese Catholics call Sunday "c=" s=, "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 s=, s= and s= 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]. 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
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 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
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".
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 , 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.