Japanese numerals

The 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 10,000. 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 yamato kotoba (native words, kun'yomi readings).

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, 二, 三). The Arabic numerals are more often used in horizontal writing, and the Chinese numerals are more common in vertical writing.

Most numbers have two readings, one derived from Chinese used for cardinal numbers (On reading) and a native Japanese reading used somewhat less formally for numbers up to 10. In some cases (listed below) the Japanese reading is generally preferred for all uses.

Number	Character	On reading	Kun reading	Preferred reading
0	零 / 〇*	rei / れい	-	zero / ゼロ
1	一	ichi / いち	hito(tsu) / ひと・つ	ichi
2	二	ni / に	futa(tsu) / ふた・つ	ni
3	三	san / さん	mit(tsu) / みっ・つ	san
4	四	shi / し	yon, yot(tsu) / よん、よっ・つ	yon
5	五	go / ご	itsu(tsu) / いつ・つ	go
6	六	roku / ろく	mut(tsu) / むっ・つ	roku
7	七	shichi / しち	nana(tsu) / なな・つ	nana
8	八	hachi / はち	yat(tsu) / やっ・つ	hachi
9	九	ku, kyū / く, きゅう	kokono(tsu) / ここの・つ	kyū
10	十	jū / じゅう	tō / とお	jū
13	十三	jū-san / じゅうさん	(tosa / とさ)	jū-san
20	二十 / 廿	ni-jū / にじゅう	(futaso / ふたそ / hata / はた)	ni-jū
30	三十 / 卅	san-jū / さんじゅう	(miso / みそ)	san-jū
40	四十	shi-jū / しじゅう	(yoso / よそ)	shi-jū
50	五十	go-jū / ごじゅう	(iso / いそ)	go-jū
60	六十	roku-jū / ろくじゅう	(muso / むそ)	roku-jū
70	七十	shichi-jū / しちじゅう	(nanaso / ななそ)	shichi-jū
80	八十	hachi-jū / はちじゅう	(yaso / やそ)	hachi-jū
90	九十	ku-jū / くじゅう	(kokonoso / ここのそ)	ku-jū
100	百	hyaku / ひゃく	(momo / もも)	hyaku
1,000	千	sen / せん	(chi / ち)	sen
10,000	万	man / まん	(yorozu / よろず)	man
100,000,000	億	oku / おく	-	oku
1,000,000,000,000	兆	chō / ちょう	-	chō
10,000,000,000,000,000	京	kei / けい	-	kei

* The special reading 〇 maru (which means "round" or "circle") is also found. It may be optionally used when reading individual digits of a number one after another, instead of as a full number. A popular example is the famous 109 store in Shibuya, Tokyo which is read as ichi-maru-kyū (Kanji: 一〇九). (It can also be read as 'ten-nine' - pronounced tō-kyū - which is a pun on the name of the Tokyu department store which owns the building.) This usage of maru for numerical 0 is similar to reading numeral 0 in English as oh. It literally means a circle. However, as a number, it is only written as 0 or rei (零). Additionally, two and five are pronounced with a long vowel in phone numbers (i.e. にい and ごお nii and goo).

Starting at 万, numbers begin with 一 (ichi) if no digit would otherwise precede. That is, 100 is just 百 hyaku, and 1000 is just 千 sen, but 10,000 is 一万 ichiman, not just *man. This differs from Chinese as numbers begin with 一 (ichi) if no digit would otherwise precede starting at 百. And, if 千 sen directly precedes the name of powers of myriad, 一 ichi is normally attached before 千 sen, which yields 一千 issen. That is, 10,000,000 is normally read as 一千万 issenman. But if 千 sen does not directly precede the name of powers of myriad or if numbers are lower than 2,000, attaching 一 ichi is optional. That is, 15,000,000 is read as 千五百万 sengohyakuman or 一千五百万 issengohyakuman, and 1,500 as 千五百 sengohyaku or 一千五百 issengohyaku.

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

On the contrary, numbers 7 and sometimes 8 are considered lucky in Japanese.

In modern Japanese, cardinal numbers are given the on readings except 4 and 7, which are called yon and nana respectively. Alternate readings are used in month names, day-of-month names, and fixed phrases. For instance, the decimal fraction 4.79 is always read yon-ten nana kyū, though April, July, and September are called shi-gatsu (4th month), shichi-gatsu (7th month), and ku-gatsu (9th month) respectively. The on readings are also used when shouting out headcounts (e.g. ichi-ni-san-shi). Intermediate numbers are made by combining these elements:

• Tens from 20 to 90 are "(digit)-jū" as in 二十 (ni-jū) to 九十 (kyū-jū).
• Hundreds from 200 to 900 are "(digit)-hyaku".
• Thousands from 2000 to 9000 are "(digit)-sen".

There are some phonetic modifications to larger numbers involving voicing or gemination of certain consonants, as typically occurs in Japanese (i.e. rendaku): e.g. roku "six" and hyaku "hundred" yield roppyaku "six hundred".

×	1	2	3	4	5	6	7	8	9	10	100	1000
100	hyaku, ippyaku	nihyaku	sanbyaku	yonhyaku	gohyaku	roppyaku	nanahyaku	happyaku	kyūhyaku	-	-	-
1,000	sen, issen	nisen	sanzen	yonsen	gosen	rokusen	nanasen	hassen	kyūsen	-	-	-
1012	itchō	nichō	sanchō	yonchō	gochō	rokuchō	nanachō	hatchō	kyūchō	jutchō*	hyakuchō	issenchō
1016	ikkei	nikei	sankei	yonkei	gokei	rokkei	nanakei	hakkei	kyūkei	jukkei*	hyakkei**	issenkei

* This also applies to multiples of 10. Change ending -jū to -jutchō or -jukkei.
** This also applies to multiples of 100. Change ending -ku to -kkei.

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

Other types of numerals

Beyond the basic cardinals and ordinals, Japanese has other types of numerals.

Distributive numbers are formed regularly from a cardinal number, a counter word, and the suffix -zutsu (ずつ), as in hitori-zutsu (一人ずつ, one person at a time, one person each).

Powers of 10

Large numbers

Following Chinese tradition, large numbers are created by grouping digits in myriads (every 10,000) rather than the Western thousands (1,000):

Rank	104	108	1012	1016	1020	1024	1028	1032	1036	1040	1044	1048	1052 or 1056	1056 or 1064	1060 or 1072	1064 or 1080	1068 or 1088
Character	万	億	兆	京	垓	𥝱, 秭	穣	溝	澗	正	載	極	恒河沙	阿僧祇	那由他, 那由多	不可思議	無量大数
Reading	man	oku	chō	kei	gai	jo, shi	jō	kō	kan	sei	sai	goku	gōgasha	asōgi	nayuta	fukashigi	muryōtaisū

Variation is due to Jinkōki, Japan's oldest mathematics text. The initial edition was published in 1627. It had many errors. Most of these were fixed in the 1631 edition. In 1634 there was yet another edition which again changed a few values. The above variation is due to inconsistencies in the latter two editions.

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 English-speaking convention. If Arabic numbers and kanji are used in combination, Western orders of magnitude may be used for numbers smaller than 10,000 (e.g. 2,500万 for 25,000,000).

In Japanese, when long numbers are written out in kanji, zeros are omitted for all powers of ten. Hence 4002 is 四千二 (in contrast, Chinese requires the use of 零 wherever a zero appears, e.g. 四千零二 for 4002). However, when reading out a statement of accounts, for example, the skipped digit or digits are sometimes indicated by tobi (飛び) or tonde (飛んで): e.g. yon-sen tobi ni or yon-sen tonde ni instead of the normal yon-sen ni.

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. The bu fractions are also used when talking about fevers - for example 九度二分 (kudonibu) for 9 and two parts - the temperature 9.2°C.

One system is as follows:

Rank	10−1	10−2	10−3	10−4	10−5	10−6	10−7	10−8	10−9	10−10
Character	分	厘	毛	糸	忽	微	繊	沙	塵	埃
Reading	bu	rin	mō	shi	kotsu	bi	sen	sha	jin	ai

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 sun.

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, in written form, 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.) In both cases, however, the reading follows the traditional system (yon-jū ni-ten ichi-kyū go kiromētoru for 42.195 kilometers; go ju-tten rei-yon pāsento for 50.04 percent.)

Formal numbers

Getabako

As with 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. Today, the numbers for one, two, three, and ten are written only in their formal form in legal documents (the numbers 4 to 9 as well as 100, 1000 and 10000 are written identically to the common ones, cf. table below). These numbers' 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). In some cases, the digit 1 is explicitly written like 壱百壱拾 for 110, as opposed to 百十 in common writing.

Formal numbers:

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

The four current banknotes of the Japanese yen, 1000-yen, 2000-yen, 5000-yen, and 10000-yen, have formal numbers 千, 弐千, 五千, and 壱万, respectively.

Old Japanese

Old Japanese shares some vocabulary with later periods, but there are also some unique numbers which are not used any more, aside from being parts of specific lexemes.

Notes:

• The transcription is based on the phoneme and is not phonetic. See Old Japanese for further information.
• See Jōdai Tokushu Kanazukai for information on subscript notation.

Number	Reading	Examples	Notes
1	pi1to2	一日 pi1to2pi1 (1 day), 一年 pi1to2to2se (1 year)
2	puta	二夜 putayo2 (2 nights)
3	mi1	三十 mi1so1 (30)
4	yo2	四十 yo2so1 (40), 四人 yo2tari (4 people)
5	itu	五年 ituto2se (5 years)
6	mu	六爪 mutuma (6 claws)
7	nana	七瀬 nanase (many rapids)	Often used to mean many.
8	ya	八雲 yakumo1 (many clouds)	Often used to mean many.
9	ko2ko2no2	九柱 ko2ko2no2pasira (9 nobles / gods)
10	to2 / to2wo	十日 to2woka (10 days)
10	so1	三十 mi1so1 (30), 四十 yo2so1 (40), 六十 muso1 (60), 八十 yaso1 (80)	Found only in compound words; not used alone.
20	pata	二十 patati (20), 二十人 patatari (20 people), 二十年 patato2se (20 years)
50	i	五十日 ika (50 days)
100	po	五百 ipo (500), 五百年 ipoto2se (500 years), 五百夜 ipoyo2 (500 nights), 八百 yapo (800), 三百 mi1po (300), 六百 mupo (600), 九百 ko2ko2no2po (900)	Used for multiple hundreds in compound numerals. Often used to mean many.
100	mo1mo1	百日 mo1mo1ka (many days)	Used for non-multiple hundred and for the number "100" by itself. Often used to mean many.
1000	ti	千年 tito2se (1000 years, many years)	Often used to mean many.
10000	yo2ro2du	八百万 yapoyo2ro2du (8000000, myriad)	Often used to mean many.

Hand counting

See also: Finger counting § Japan

Japanese uses separate systems for counting for oneself and for displaying numbers to others, which both proceed up to ten. For counting, one begins with the palm open, then counts up to five by curling up (folding down) the fingers, starting from the thumb – thus one has just the thumb down (and others extended), while four has only the pinkie extended, and five has a fist. One then counts up to ten by proceeding in the reverse order, extending the fingers, starting at the pinkie – thus six is the same as four, seven the same as three, and so forth, with ten ending with the palm open. While this introduces ambiguity, it is not used to present to others, so this is generally not a problem. When displaying for others, one starts with the hand closed, and extends fingers, starting with the index, going to the pinkie, then ending with the thumb, as in the United States. For numbers above five, one uses an open hand (indicating five) and places the appropriate number of fingers from the other hand against the palm (palms facing each other) – so six has the index finger against the palm, and so forth. To display ten, one presents both hands open and palm outwards.

Numbers in Japanese words

Since the adoption of Arabic numerals, numbers have become written in Arabic numerals more and more often. Counters and ordinal numbers are typically written in Arabic numbers, such as 3人 (three people), 7月 (July, "seventh-month"), 20歳 (age 20), etc., although 三人、七月、and 二十歳 are also acceptable to write (albeit less common). However, numbers that are part of lexemes are typically written in kanji. For example, the term yaoya 八百屋 (tr.: vegetable stand / grocer) translates into "800 store", uses the Old Japanese pronunciation for 800, ya(h)o. The notorious Japanese national gang, the yakuza, can be written 八九三 (or 893), a hand in oicho-kabu that is worth 0 points, indicating that yakuza are "worthless persons" or "gambling persons".

See also

• Decimal mark
• Japanese counter word
• Japanese people

External links

• (in Japanese) 大数の名前について
• Ancient Japanese number system
• English exercises for learning Japanese numerals
• Audio to learn the pronunciation for Japanese numbers
• Convert kanji numerals to arabic numerals (sci.lang.Japan FAQ page)
• Convert arabic numerals to kanji numerals (sci.lang.Japan FAQ page)