Chinese numerals are characters for writing numbers in Chinese. Today speakers of Chinese use three numeral systems: the Indian (Arabic) system used world-wide and two indigenous systems.
The more familiar indigenous system are 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 primarily use the Indian (Arabic) system for convenience, with traditional Chinese numerals used in finance, mainly for writing amounts on checks and banknotes and some ceremonial occasions.][
The other indigenous system is the Suzhou numerals, or huama, a positional system. It is the only surviving form of the rod numerals. They were once used by Chinese mathematicians, and later in Chinese markets, such as those in Hong Kong before the 1990s, but has been gradually supplanted by the Arabic numerals and also the Roman numerals.
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.
There are characters representing the numbers zero through nine, and other characters representing larger numbers such as tens, hundreds, thousands and so on. There are two sets of characters for Chinese numerals: one for everyday writing and one for use in commercial or financial contexts known as dàxiě (simplified Chinese: ; traditional Chinese: ). The latter arose because the characters used for writing numerals are geometrically simple, so simply using those numerals cannot prevent forgeries in the same way spelling numbers out in English would. A forger could easily change everyday characters 三十 (30) to 五千 (5000) by adding just a few strokes. That would not be possible when writing using the financial characters 參拾 (30) and 伍仟 (5000). 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, S denotes Simplified Chinese characters.
In the PLA, some numbers will have altered names when used for clearer radio communications. They are:
Similar 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, 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 number is 10,000 (myriad, 萬 wàn) times the previous:
In practice, this situation does not lead to ambiguity, with the exception of 兆 (zhào), which means 1012 according to the second system in common usage throughout the Chinese communities as well as in Japan and Korea, but is also used for 106 in recent years (esp. in mainland China to represent the Megabyte). To avoid problems arising from the ambiguity, the PRC government never uses this character in official documents, but uses 万亿 (wànyì) instead. The ROC government in Taiwan uses 兆 (zhào) to mean 1012 in official documents.
Numerals beyond 載 zài come from Buddhist texts in Sanskrit, but are mostly found in ancient texts.
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.
攸 (T) or 幺 (S) corresponds to the SI prefix yocto-.
介 (T) or 仄 (S) corresponds to the SI prefix zepto-.
阿 corresponds to the SI prefix atto-.
飛 (T) or 飞 (S) corresponds to the SI prefix femto-.
皮 corresponds to the SI prefix pico-.
奈 (T) or 纳 (S) corresponds to the SI prefix nano-.
still in use, corresponds to the SI prefix milli-.
still in use, corresponds to the SI prefix centi-.
In the People's Republic of China, the translations for the SI prefixes in 1981 were different from those used today. The larger (兆, 京, 垓, 秭, 穰) and smaller Chinese numerals (微, 纖, 沙, 塵, 渺) were defined as translations for the SI prefixes as mega, giga, tera, peta, exa', micro, nano, pico, femto, atto, resulting in the creation of more values for each numeral.
In addition, Taiwanese defined 百萬 as the translation for mega. This translation is widely used in official documents, academic communities, informational industries, etc. However, the civil broadcasting industries sometimes use 兆赫 to represent "megahertz".
Today, both the governments of the People's Republic of China (Mainland China, Hong Kong and Macau) and Republic of China (Taiwan) use phonetic transliterations for the SI prefixes. However, the governments have each chosen different Chinese characters for certain prefixes. The following table lists the two different standards together with the early translation.
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 greater than 200 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 the southern Min dialect of Chaozhou (Teochew), 兩 (no6) is used to represent the "2" numeral in all numbers from 200 onwards. Thus:
For the numbers 11 through 19, the leading "one" (一) is usually omitted. In some dialects, like Shanghainese, when there are only two significant digits in the number, the leading "one" and the trailing zeroes are omitted. Sometimes, the one before "ten" in the middle of a number, such as 213, is omitted. Thus:
In certain older texts like the Protestant Bible or in poetic usage, numbers such as 114 may be written as    (百十四).
For numbers larger than a myriad, the same grouping system used in English applies, except in groups of four places (myriads) rather than in groups of three (thousands). Hence it is more convenient to think of numbers here as in groups of four, thus 1,234,567,890 is regrouped here as 12,3456,7890. Larger than a myriad, each number is therefore four zeroes longer than the one before it, thus 10000 × wàn (萬) = yì (億). 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):
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:
To construct a fraction, the denominator is written first, followed by 分之 ("parts of") and then the numerator. This is the opposite of how fractions are read in English, which is numerator first. Each half of the fraction is written the same as a whole number. Mixed numbers are written with the whole-number part first, followed by 又 ("and"), then the fractional part.
Percentages are constructed similarly, using 百 (100) as the denominator. The 一 (one) before 百 is omitted.
Decimal numbers are constructed by first writing the whole number part, then inserting a point (simplified Chinese: ; traditional Chinese: ; pinyin: diǎn), and finally the decimal expression. The decimal expression is written using only the digits for 0 to 9, without multiplicative words.
Ordinal numbers are formed by adding 第 ("sequence") before the number.
Negative numbers are formed by adding fù (simplified Chinese: ; traditional Chinese: ) before the number.
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 (simplified Chinese: ; traditional Chinese: ; pinyin: Sūzhōu huāmǎ) 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.
Ancient Chinese used positional decimal counting rod numerals for calculation since the Spring and Autumn period.
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.
In the 1930s, archeologist Pei Wenzhong unearthed Upper Cave Man relics in Zhoukoudian,
Most Chinese numerals of later period were descendants from Shang dynasty oracle numerals of 14th century B.C. The oracle bone script numerals were found on tortoise shell and animal bones.
Some of the bronze script numerals such as 1, 2, 3, 4, 10, 11, 12, and 13 were passed to Rod numerals.
while horizontal rod numbers are used for the tens, thousands, hundred thousands etc. Sun Tzu wrote 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 Han dynasty to 16th century. In early civilizations, the Shang were able to express any numbers, however large with only 9 symbols and a counting board.
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 Ming and Qing dynasties (when Arabic numerals were first introduced into China), some Chinese mathematicians used Chinese numeral characters as positional system digits. After Qing dynasty, both the Chinese numeral characters and the Suzhou numerals were replaced by Arabic numerals in mathematical writings.
Traditional Chinese numeric characters are also used in Japan and Korea 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.