Japanese numerals

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Template:Table Numeral SystemsThe system of Japanese numerals is the system of number names used in the Japanese language. The Japanese numerals in writing are entirely based on the Chinese numerals and the grouping of large numbers follow the Chinese tradition of grouping by 10000. Two sets of pronunciations for the numerals exist in Japanese, one is based on Sino-Japanese (on'yomi) readings of the Chinese characters and the other is based on the Japanese kun'yomi readings.

1 Basic numbering in Japanese
2 Powers of 10
- 2.1 Large numbers
- 2.2 Decimal fractions
3 Formal numbers
4 See also
5 External links

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Basic numbering in Japanese

There are two ways of writing the numbers in Japanese, in Arabic numerals (1, 2, 3) or in Chinese numerals (一, ニ, 三). The Arabic numerals are more often used in horizontal writing, and the Chinese numerals are more common in vertical writing.

(Some numbers have multiple names.)

Number	Character	Preferred reading	On reading	Kun reading
0	零／〇	zero	rei / れい	(none)
1	一	ichi	ichi / いち	hito(tsu) / ひと(つ)
2	二	ni	ni, ji / に、じ	futa(tsu) / ふた(つ)
3	三	san	san / さん	mi(ttsu) / み(っつ)
4	四	yon	shi / し	yo(ttsu) / よ(っつ)
5	五	go	go / ご	itsu(tsu) / いつ(つ)
6	六	roku	roku / ろく	mu(ttsu) / む(っつ)
7	七	nana	shichi / しち	nana(tsu) / なな(つ)
8	八	hachi	hachi / はち	ya(ttsu) / や(っつ)
9	九	kyū	kyū, ku / きゅう、く	kokono(tsu) / ここの(つ)
10	十	jū	jū / じゅう	tō / とお
20	二十	nijū	nijū / にじゅう	hata(chi) / はた(ち)
100	百	hyaku	hyaku / ひゃく	(momo / もも)
1,000	千	sen	sen / せん	(chi / ち)
10,000	万	man	man / まん	(yorozu / よろず)
8,000,000	八百万	happyakuman	happyakuman	(yaoyorozu* / やおよろず)

* There is no evidence that 8 million was called yaoyorozu in ancient Japanese. Rather it simply meant many, like myriad.

The numbers 4 and 9 are considered unlucky in Japanese: 4, pronounced shi, is a homophone for "death"; 9, when pronounced ku, is a homophone for "suffering." The number 13 is sometimes considered unlucky, though this is a carryover from Western tradition.

In modern Japanese, the kun readings are only used for single digit numbers and day-of-month names, although in many contexts the on readings will be used instead. Intermediate numbers are made by combining these elements:

Tens from 20 to 90 are "(digit)-jū".
Hundreds from 200 to 900 are "(digit)-hyaku".
Thousands from 2000 to 9000 are "(digit)-sen".
Additionally, the tens from 30 to 90 in kun reading are formed by "(digit)-so", where the digit is also in kun reading: miso (30), yoso (40), iso (50), muso (60), nanaso (70), yaso (80), kokonoso (90). Variations include i for 50 and the suffix -ji for 20 through 90. However, for the most part, these are not in use in modern Japanese.

There are some phonetic modifications to larger numbers, but they are a minor detail.

In large numbers, elements are combined from largest to smallest, and zeros are implied.

Number	Character	Reading
11	十一	jū ichi
17	十七	jū nana, jū shichi
151	百五十一	hyaku go-jū ichi
302	三百二	san-byaku ni
469	四百六十九	yon-hyaku roku-jū kyū
2025	二千二十五	ni-sen ni-jū go

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Powers of 10

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Large numbers

Following Chinese tradition, large numbers are created by grouping digits in myriads (every 10,000) rather than the Western thousands (1000):

Rank	10⁴	10⁸	10¹²	10¹⁶	10²⁰
Character	万	億	兆	京	垓
Name	man	oku	chō	kei	gai

Examples: (spacing by groups of four digits is given only for clarity of explanation)
1 0000 : 一万 : ichi-man
983 6703 : 九百八十三万六千七百三 : kyū-hyaku hachi-jū san man, roku-sen nana-hyaku san
20 3652 1801 : 二十億三千六百五十二万千八百一 : ni-jū oku, san-zen rop-pyaku go-jū ni-man, sen hap-pyaku ichi

However, numbers written in Arabic numerals are separated by commas every three digits following Western convention.

In Japanese, when long numbers are written out in kanji, zeros are omitted for all powers of ten. Hence 302 is 三百二. In contrast, Chinese requires the use of 零 wherever a zero appears, e.g. 三百零二 for 302.

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Decimal fractions

Japanese has two systems of numerals for decimal fractions. They are no longer in general use, but are still used in some instances such as batting and fielding averages of baseball players, winning percentages for sports teams, and in some idiomatic phrases (such as 五分五分の勝負 "fifty-fifty chance"), and when representing a rate or discount.

One system is as follows:

Japanese name (romaji)	Japanese name (kanji)	Fraction
bu	分	one tenth; 10^-1
rin	厘	one hundredth; 10^-2
mō	毛	one thousandth; 10^-3
shi	糸	10^-4
kotsu	忽	10^-5

This is the system used with the traditional Japanese units of measurement. Several of the names are used "as is" to represent a fraction of a shaku.

The other system of representing these decimal fractions of rate or discount uses a system "shifted down" with a bu becoming a "one hundredth" and so on, and the unit for "tenth" becoming wari:

Rank	10^-1	10^-2	10^-3	10^-4	10^-5
Character	割	分	厘	毛	糸
Reading	wari	bu	rin	mō	shi

This is often used with prices. For example:
一割五分引き ichi-wari go-bu biki "15% discount"
打率三割八分九厘 daritsu san-wari hachi-bu kyū-rin "batting average .389"

With the exception of wari, these are rarely seen in modern usage. Decimal fractions are typically written with either kanji numerals (vertically) or Arabic numerals (horizontally), preceded by a decimal point, and are read as successive digits, as in Western convention. Note that they can be combined with either the traditional system of expressing numerals (42.195 kilometers: 四十二・一九五キロメートル), in which powers of ten are written, or with the place value system, which uses zero (50.04 percent: 五〇・〇四パーセント).

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Formal numbers

Like in Chinese numerals, there exists in Japanese a separate set of kanji for numerals called daiji (大字) used in legal and financial documents to prevent unscrupulous individuals from adding a stroke or two, turning a one into a two or a three. The formal numbers are identical to the Chinese formal numbers except for minor stroke variations. Some formal numbers are obsolete and not used in legal documents today. Those that remain are the ones whose common forms can be changed to a higher value by adding strokes (1 and 2 were explained above, while 3 can be changed to 5, and 10 to 1000). The digit 1 is explicitely written like 壱百壱拾 for 110, as opposed to 百十 in common writing.

Formal numbers:

Number	Common	Formal
Number	Common	Modern	Obsolete
1	一	壱	壹
2	二	弐	貳
3	三	参	參
4	四		肆
5	五		伍
6	六		陸
7	七		柒 (漆)
8	八		捌
9	九		玖
10	十	拾	拾
100	百		佰
1000	千		阡 (仟)
10000	万	萬	萬