The Chinese numeral system is a system of words used to describe numbers in the Chinese language, as well as other languages that use Chinese characters, primarily Japanese and Korean.
The Chinese numeral system is a positional decimal system. There are characters for the numbers from zero through ten, and then characters for the powers of 10 thereafter.
In Chinese, the power-of-ten numbers are used as suffixes to the basic numerals. For example, 二十 is 20, because 十 marks the place value of the 二. 一百二十三 is 123, because 百 is prefixed with a 一, 十 is prefixed with a 二, and 三 is at the end of the number. If the place value is 一十, then the 一 is usually omitted, so 13 is 十三, not 一十三. Any zeros are expressed using a single 零 without any place value markers. So 103 is 一百零三, and 10003 is 一万零三.
In Japanese, a 一 can be omitted before any place-value marker, not just 十, and 零 is not used as a positional placeholder, so 100 is just 百, 103 is simply 百三, and 123 is just 百二十三.
The symbols 十, 百, and 千 are themselves repeated after 万, so 100,000 is 十万, and 1,230,000 is 一百二十三万.
In certain cases, the word 二 can be replaced with 兩 (两 in simplified Chinese, 両 in shinjitai kanji) to mean "two", usually when talking about counts of objects (e.g. 两个人 for "two people", or 两只猫 for "two cats"). However, using 二 for standalone numbers is always correct. However, when using two as an prefix before a number larger than hundred, 两 should be used. For example, 两千两白二十 is correct for 2,220. The use of 两 is sometimes very important, because for example 二百五 means 'idiot' or 'very stupid person', while the correct version 两百五 is just 205 as it should be.
Numbers larger than 亿 are not generally used in daily life. The Wujing Suanshu defines a series of numbers larger than 亿, and assigns three different scales to them:
- The "lower numbers" (下數 (Traditional), 下数 (Simplified)), in which each character after 万 is valued 10 times the previous one. In this system, 亿 is equal to 105.
- The "middle numbers" (中數 (Traditional), 中数 (Simplified)), in which each character after 亿 is valued 108 (一亿) times the previous one.
- The "upper numbers" (上數 (Traditional), 上数 (Simplified)), in which each character after 万 is the square of the previous one.
In modern times, these numbers have been redefined such that each character after 万 is valued 104 (一万) times the previous one, giving a fourth system.
The higher numerals are as follows:
Examples of usage
In the above examples, each way of counting has its own grouping systems. Below are some examples of the usage of these systems.
In the lower numbers, each power of 10 has its own positional marker.
The lower numbers can express numbers with up to 15 digits. After that, the symbols are undefined.
In modern usage, 十, 百, and 千 repeat after 万, and each of them again once after each symbol afterward.
From here onwards, a group of four digits will be implied to have 千, 百, and 十 in between them.
|264 - 1||1844京6744兆0737亿0955万1615|
|30! + 116||2溝6525穰2859秭8121垓9105京8636兆3084亿8177万1561|
This system can express numbers with up to 48 digits.
In the middle numbers, 十, 百, and 千 repeat after 万, and 万 repeats once after each symbol afterward.
|264 - 1||1844兆6744万0737亿0955万1615|
|30! + 116||2垓6525万2859京8121万9105兆8636万3084亿8177万1561|
The middle numbers can express numbers with up to 88 digits.
In the upper numbers, each symbol 万 and above repeats once between occurrences of the next higher symbol, in a fractal-like pattern.
|264 - 1||1844兆6744万0737亿0955万1615|
|30! + 116||2京6525万2859亿8121万9105兆8636万3084亿8177万1561|
The upper numbers can express numbers with up to 8192 digits.
Numbers larger than 载 appear in some Buddhist texts, which are not defined in the Wujing Suanshu. In Chinese, they are not used; however, some of them have been standardized in Japanese usage. A list is given below with the hypothetical values that the upper numbers would have if the system in thet Wujing Suanshu were extended to include these numbers.
|极/極||extreme, the limit||jí||goku||1048||108,192|
|恒河沙/恆河沙||The sands of the Ganges River||héng hé shā||gōgasha||1052||1016,384|
|阿僧祇||Asamkhyeya||ā sēng qí||asōgi||1056||1032,768|
|那由他||Nayuta, figuratively "myriad" in Sanskrit||nà yóu tā||nayuta||1060||1065,536|
|不可思议/不可思議||unimaginable, inconceivable||bù kě sī yì||fukashigi||1064||10131,072|
|无量大数/無量大数||immeasurably large number||wú liàng dà shù||muryōtaisū||1068||10262,144|
- 不可說不可說轉 (The Chinese article on Nirabhilapya nirabhilapya parivarta with a list of Chinese numerals)
- 不可説不可説転 (The Japenese article on Nirabhilapya nirabhilapya parivarta with a list of Chinese numerals)
- 大数系统, a section in article 中文数字, on 维基百科 (Chinese Wikipedia). http://zh.wikipedia.org/wiki/%E4%B8%AD%E6%96%87%E6%95%B0%E5%AD%97#.E5.A4.A7.E6.95.B8.E7.B3.BB.E7.B5.B1
- 大数系统, a section in article 日语数字, on 维基百科 (Chinese Wikipedia). http://zh.wikipedia.org/wiki/%E6%97%A5%E8%AA%9E%E6%95%B8%E5%AD%97#.E5.A4.A7.E6.95.B8.E7.B3.BB.E7.B5.B1