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.
Basic numbers[]
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.
|
Numeral |
Value |
Chinese pronunciation (Mandarin, pinyin) |
Japanese pronunciation |
|---|---|---|---|
| 零 | 0 | líng | rei, zero |
| 一 | 1 | yī | ichi |
| 二 | 2 | èr | ni |
| 三 | 3 | sān | san |
| 四 | 4 | sì | shi, yon |
| 五 | 5 | wǔ | go |
| 六 | 6 | liù | roku |
| 七 | 7 | qī | shichi, nana |
| 八 | 8 | bā | hachi |
| 九 | 9 | jiǔ | kyū |
| 十 | 10 | shí | jū |
| 百 | 100 | bǎi | hyaku |
| 千 | 1,000 | qiān | sen |
| 万/萬 | 10,000 | wàn | man |
| 亿/億 | 108 | yì | oku |
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, 两千两百二十 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 两百五 (although 两百五十 is more unambiguous and grammatically correct) is just 250 as it should be.
Large numbers[]
Numbers larger than 亿 are not generally used in daily life. The Wujing Suanshu[1] 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:
| Numeral | Non-numeric
meaning/definition |
Chinese pinyin | Japanese | Lower
numbers |
Modern
usage |
Middle
numbers |
Upper
numbers |
|---|---|---|---|---|---|---|---|
| 兆 | omen | zhào | chō | 106 | 1012 | 1016 | 1016 |
| 京 | capital | jīng | kei | 107 | 1016 | 1024 | 1032 |
| 垓 | border, frontier | gāi | gai | 108 | 1020 | 1032 | 1064 |
| 秭 | zǐ | shi/jo | 109 | 1024 | 1040 | 10128 | |
| 穣/穰 | abundant, lush | ráng | jō | 1010 | 1028 | 1048 | 10256 |
| 沟/溝 | ditch, canal | gōu | kō | 1011 | 1032 | 1056 | 10512 |
| 涧/澗 | brook, stream | jiàn | kan | 1012 | 1036 | 1064 | 101,024 |
| 正 | upright, righteous | zhèng | sei | 1013 | 1040 | 1072 | 102,048 |
| 载/載 | load, debt | zài | sai | 1014 | 1044 | 1080 | 104,096 |
The upper numbers are the same as Knuth's -yllion system, with 亿 being one myllion, 兆 being one byllion, and so on.
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.
Lower numbers[]
In the lower numbers, each power of 10 has its own positional marker.
| Number | Representation |
|---|---|
| 647,890 | 六亿四万七千八百九十 |
| 123,456,789,012 | 一溝二穰三秭四垓五京六兆七亿八万九千零一十二 |
The lower numbers can express numbers with up to 15 digits. After that, the symbols are undefined.
Modern usage[]
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.
| Number | Representation |
|---|---|
| 647,890 |
六十四万七千八百九十 (64万7890) |
| 123,456,789,012 | 一千二百三十四亿五千六百七十八万九千零一十二 (1234亿5678万9012) |
| 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.
Middle numbers[]
In the middle numbers, 十, 百, and 千 repeat after 万, and 万 repeats once after each symbol afterward.
| Number | Representation |
|---|---|
| 647,890 | 64万7890 |
| 123,456,789,012 | 1234亿5678万9012 |
| 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 |
| ceil(e5π√163) | 1247万2571載5601万9637正3048万5610澗7520万0180溝7455万2566穰8245万
8586秭2995万2721垓7336万8815京7940万8549兆5792万2996亿2109万3744 |
The middle numbers can express numbers with up to 88 digits.
Upper numbers[]
In the upper numbers, each symbol 万 and above repeats once between occurrences of the next higher symbol, in a fractal-like pattern.
| Number | Representation |
|---|---|
| 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 |
| RSA-100 | 1522京6050万2792亿2533万3605兆3561万8378亿1326万3742垓9718万0681亿1496万1380兆6886万5790亿8494万5801京2296万3258亿9528万 9765兆4000万3506亿9200万6139 |
| 108,191 | 1千万亿兆京垓秭穰溝澗正載 |
The upper numbers can express numbers with up to 8192 digits.
Larger numbers[]
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.[2] 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.
| Numeral | Non-numeric
meaning/definition |
Chinese
pinyin |
Japanese | Modern
usage |
Upper
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 |
See Also[]
- 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)
External Links[]
Denis Maksudov. Online converter of numbers to different numeral systems. Chinese numerals
References[]
- ↑ 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
Indian counting system: Lakh · Crore · Padma · Tallakshana · Ogha · Ababa · Atata · Sogandhika · Uppala · Dvajagravati · Kumuda · Pundarika · Paduma · Kathana · Mahakathana · Asankhyeya · Dvajagranisamani · Vahanaprajnapti · Inga · Kuruta · Sarvanikshepa · Agrasara · Uttaraparamanurajahpravesa · Avatamsaka Sutra · Nirabhilapya nirabhilapya parivarta · Jaghanya Parīta Asaṃkhyāta
Chinese, Japanese and Korean counting system: Wan · Yi · Zhao · Jing · Gai · Zi · Rang · Gou · Jian · Zheng · Zai · Ji · Gougasha · Asougi · Nayuta · Fukashigi · Muryoutaisuu
See also: Template:Googology in Japan