|Hindu-Arabic numeral system|
|Positional systems by base|
|Non-standard positional numeral systems|
|List of numeral systems|
The Japanese numerals are the number names used in Japanese. In writing, they are the same as the Chinese numerals, and large numbers follow the Chinese style of grouping by 10,000. Two pronunciations are used: the Sino-Japanese (on'yomi) readings of the Chinese characters and the Japanese yamato kotoba (native words, kun'yomi readings).
There are two ways of writing the numbers in Japanese: in Arabic numerals (1, 2, 3) or in Chinese numerals (?, ?, ?). 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 (Kun reading) used somewhat less formally for numbers up to 10. In some cases (listed below) the Japanese reading is generally preferred for all uses. Archaic readings are marked with +.
|Number||Character||On reading||Kun reading||Preferred reading|
|0||? / ?*||rei /||--||zero / (loanword, gairaigo)|
|1||?||ichi /||hito(tsu) / ?||ichi|
|2||?||ni / ?||futa(tsu) / ?||ni|
|3||?||san /||mit(tsu) / ?||san|
|4||?||shi / ?||yon, yot(tsu) / ?||yon|
|5||?||go / ?||itsu(tsu) / ?||go|
|6||?||roku /||mut(tsu) / ?||roku|
|7||?||shichi /||nana(tsu) / ?||nana|
|8||?||hachi /||yat(tsu) / ?||hachi|
|9||?||ku, ky? / ?,||kokono(tsu) /||ky?|
|10||?||j? /||t? /||j?|
|20||ni-j? / ?||(hata / )+||ni-j?|
|30||san-j? /||(miso / )+||san-j?|
|40||shi-j? / ?||(yoso / )+||yon-j?|
|50||go-j? / ?||(iso / )+||go-j?|
|60||roku-j? /||(muso / )+||roku-j?|
|70||shichi-j? /||(nanaso / )+||nana-j?|
|80||hachi-j? /||(yaso / )+||hachi-j?|
|90||ku-j? / ?||(kokonoso / ?)+||ky?-j?|
|100||?||hyaku /||(momo / )+||hyaku|
|500||go-hyaku / ?||(io / )+||go-hyaku|
|800||hap-pyaku /||(yao / )+||hap-pyaku|
|1,000||?||sen /||(chi / ?)+||sen|
|10,000||?||man /||(yorozu / )+||man|
* The special reading ? 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-ky? (Kanji: ). (It can also be read as 'ten-nine'--pronounced t?-ky?--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. However, as a number, it is only written as 0 or rei (?). Additionally, two and five are pronounced with a long vowel in phone numbers (i.e. and nii and goo).
Starting at ? (10,000), numbers begin with ? (ichi) if no digit would otherwise precede. That is, 100 is just ? hyaku, and 1000 is just ? sen, but 10,000 is ichiman, not just *man. (This differs from Chinese, where numbers begin with ? if no digit would otherwise precede starting at 100.) And, if ? sen directly precedes the name of powers of myriad, ? ichi is normally attached before ? sen, which yields issen. That is, 10,000,000 is normally read as issenman. But if ? sen does not directly precede the name of powers of myriad or if numbers are lower than 2,000, attaching ? ichi is optional. That is, 15,000,000 is read as ? sengohyakuman or issengohyakuman, and 1,500 as sengohyaku or ? issengohyaku.
As noted above, yon (4) and nana (7) are preferred to shi and shichi. It is purported that this is because shi is also the reading of the word ? ("death") which makes it an unlucky reading; while shichi may sound too similar to ichi (1), shi or hachi (8). However, in quite a number of established words and phrases, shi and shichi are preferred; additionally, when counting (as in "ichi, ni, san, shi,..."), shi and shichi may be preferred.
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 (?). See tetraphobia. The number 13 is sometimes considered unlucky, though this is a carryover from Western tradition. In contrast, 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 ky?, 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:
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".
* This also applies to multiples of 10. Change ending -j? to -jutch? 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.
|17||j? nana, j? shichi|
|151||?||hyaku go-j? ichi|
|469||yon-hyaku roku-j? ky?|
|2025||ni-sen ni-j? go|
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 (), as in hitori-zutsu (?, one person at a time, one person each).
Following Chinese tradition, large numbers are created by grouping digits into myriads (every 10,000) rather than the Western thousands (1,000):
Variation is due to the Jink?ki (), 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. There are different characters for 1024 (of which ? is in Chinese today), and after 1048 they differ in whether they continue increasing by a factor of 104 or switch to 108. (If by a factor of 108, the intervening factors of 104 and produced with ? man. The current edition of the Jink?ki, the 11th, follows a factor of 104 throughout, though individuals even today some people use the values from the 8th edition.)
The first three numbers with multisyllabic names and variation in assigned values ultimately derive from India, though they did not have defined values there. g?gasha was originally used in Buddhist scripture for an indefinitely large quantity; it derives from gang? 'Ganges' (which conveniently includes the character ? ka 'river') and ? sha 'sand', referring to the innumerable sands of the Ganges River. as?gi, from Sanskrit asa?khyeya 'uncountable/innumerable', with the negative prefix ? a, and nayuta is from Sanskrit ?/ nayuta(h). After that, the numbers are Buddhist terms translated into or coined in Chinese and later assigned numerical values fukashigi 'unimaginable' and ? mury?tais? 'immeasurably large number'.
Examples: (spacing by groups of four digits is given only for clarity of explanation)
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? 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 (in contrast, Chinese requires the use of ? wherever a zero appears, e.g. ? for 4002). However, when reading out a statement of accounts, for example, the skipped digit or digits are sometimes indicated by tobi () or tonde (): e.g. yon-sen tobi ni or yon-sen tonde ni instead of the normal yon-sen ni.
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 ? "fifty-fifty chance"), and when representing a rate or discount. The bu fractions are also used when talking about fevers--for example ? (kudonibu) for 9 and two parts--the temperature 9.2°C.
One system is as follows:
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:
This is often used with prices. For example:
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 ), in which powers of ten are written, or with the place value system, which uses zero (50.04 percent? .) In both cases, however, the reading follows the traditional system (yon-j? ni-ten ichi-ky? go kirom?toru for 42.195 kilometers; go ju-tten rei-yon p?sento for 50.04 percent.)
As with Chinese numerals, there exists in Japanese a separate set of kanji for numerals called daiji () 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 ? for 110, as opposed to in common writing.
The four current banknotes of the Japanese yen, 1000-yen, 2000-yen, 5000-yen, and 10000-yen, have formal numbers ?, , , and , respectively.
|1||pi1to2||pi1to2pi1 (1 day), pi1to2to2se (1 year)|
|2||puta||putayo2 (2 nights)|
|4||yo2||yo2so1 (40), yo2tari (4 people)|
|5||itu||ituto2se (5 years)|
|6||mu||mutuma (6 claws)|
|7||nana||nanase (many rapids)||Often used to mean many.|
|8||ya||yakumo1 (many clouds)||Often used to mean many.|
|9||ko2ko2no2||ko2ko2no2pasira (9 nobles / gods)|
|10||to2 / to2wo||to2woka (10 days)|
|10||so1||mi1so1 (30), yo2so1 (40), muso1 (60), yaso1 (80)||Found only in compound words; not used alone.|
|20||pata||patati (20), patatari (20 people), patato2se (20 years)|
|50||i||ika (50 days)|
|100||po||ipo (500), ipoto2se (500 years), ipoyo2 (500 nights), yapo (800), mi1po (300), mupo (600), ko2ko2no2po (900)||Used for multiple hundreds in compound numerals. Often used to mean many.|
|100||mo1mo1||mo1mo1ka (many days)||Used for non-multiple hundred and for the number "100" by itself. Often used to mean many.|
|1000||ti||tito2se (1000 years, many years)||Often used to mean many.|
|10000||yo2ro2du||yapoyo2ro2du (8000000, myriad)||Often used to mean many.|
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.
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? (three people), 7? (July, "seventh-month"), 20? (age 20), etc., although and 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 (tr.: vegetable stand / grocer) translates into "800 store", uses the Old Japanese pronunciation for 800, ya(h)o. The notorious Japanese organized crime syndicate, the yakuza, can be written (or 893), a hand in oicho-kabu that is worth 0 points, indicating that yakuza are "worthless persons" or "gambling persons".