Chinese numeral system

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.
== Large numbers ==
Numbers larger than 亿 are not generally used in daily life. The Wujing Suanshu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 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.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 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 ==
Category:Googology in Asia