Japanese numerals
Encyclopedia
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).
(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.
Some numbers have multiple names.
* The special reading maru (which means "round" or "circle") is also found. It is 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. (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 .
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.
The numbers 4 and 9 are considered unlucky in Japanese: 4, pronounced shi, is a homophone for ; 9, when pronounced ku, is a homophone for . See tetraphobia
. The number 13 is sometimes considered unlucky, though this is a carryover from Western tradition
.
In modern Japanese, the digits 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. 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".
In large numbers, elements are combined from largest to smallest, and zeros are implied.
* Hyaku becomes byaku due to rendaku
.
s (every 10,000) rather than the Western thousands (1000):
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)
However, numbers written in Arabic numerals are separated by commas every three digits following Western 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, in reading, the digit zero is sometimes pronounced as tobi (飛び) or tonde (飛んで) to indicate the lack of numbers, e.g. yon-sen tobi ni or yon-sen tonde ni can be used instead of the normal yon-sen ni.
One system is as follows:
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:
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: 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:
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.
shares some vocabulary with later periods, but there are also some unique numbers which are not used any more.
Notes:
Number names
In linguistics, number names are specific words in a natural language that represent numbers.In writing, numerals are symbols also representing numbers...
used in the Japanese language
Japanese language
is a language spoken by over 130 million people in Japan and in Japanese emigrant communities. It is a member of the Japonic language family, which has a number of proposed relationships with other languages, none of which has gained wide acceptance among historical linguists .Japanese is an...
. The Japanese numerals in writing are entirely based on the Chinese numerals
Chinese numerals
Chinese numerals are characters for writing numbers in Chinese. Today speakers of Chinese use three numeral systems:the ubiquitous Arabic numerals and two indigenous systems....
and the grouping of large numbers follow the Chinese
China
Chinese civilization may refer to:* China for more general discussion of the country.* Chinese culture* Greater China, the transnational community of ethnic Chinese.* History of China* Sinosphere, the area historically affected by Chinese culture...
tradition
Culture of China
Chinese culture is one of the world's oldest and most complex. The area in which the culture is dominant covers a large geographical region in eastern Asia with customs and traditions varying greatly between towns, cities and provinces...
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
Yamato kotoba
are native Japanese words, meaning those words in Japanese that have been inherited from Old Japanese, rather than being borrowed at some stage. They are also known as...
(native words, kun'yomi readings).
Basic numbering in Japanese
There are two ways of writing the numbers in Japanese, in Arabic numeralsArabic numerals
Arabic numerals or Hindu numerals or Hindu-Arabic numerals or Indo-Arabic numerals are the ten digits . They are descended from the Hindu-Arabic numeral system developed by Indian mathematicians, in which a sequence of digits such as "975" is read as a numeral...
(1, 2, 3) or in Chinese numerals
Chinese numerals
Chinese numerals are characters for writing numbers in Chinese. Today speakers of Chinese use three numeral systems:the ubiquitous Arabic numerals and two indigenous systems....
(一, 二, 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 0 (number) 0 is both a numberand the numerical digit used to represent that number in numerals.It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems... |
零 / 〇* | zero | rei / れい | zero / ぜろ |
| 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 | yon, yo(ttsu) / よん、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 10 (number) 10 is an even natural number following 9 and preceding 11.-In mathematics:Ten is a composite number, its proper divisors being , and... |
十 | jū | jū / じゅう | tō / とお |
| 20 20 (number) 20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.-In mathematics:*20 is the basis for vigesimal number systems.... |
二十 | ni-jū | ni-jū / にじゅう | hata(chi) / はた・ち |
| 30 30 (number) 30 is the natural number following 29 and preceding 31.-In mathematics:30 is the sum of the first four squares, which makes it a square pyramidal number.It is a primorial and is the smallest Giuga number.... |
三十 | san-jū | san-jū / さんじゅう | miso / みそ |
| 100 100 (number) 100 is the natural number following 99 and preceding 101.-In mathematics:One hundred is the square of 10... |
百 | hyaku | hyaku / ひゃく | (momo / もも) |
| 1,000 | 千 | sen | sen / せん | (chi / ち) |
| 10,000 10000 (number) 10000 is the natural number following 9999 and preceding 10001.-Name:Many languages have a specific word for this number: In English it is myriad, in Ancient Greek , in Aramaic , in Hebrew רבבה , in Chinese , in Japanese [man], in Korean [man], and in Thai หมื่น [meun]... |
万 | man | man / まん | (yorozu / よろず) |
| 100,000,000 100000000 (number) One hundred million is the natural number following 99999999 and preceding 100000001.In scientific notation, it is written as 108.... |
億 | oku | oku / おく | - |
| 1,000,000,000,000 | 兆 | chō | chō / ちょう | - |
Shibuya, Tokyo
is one of the 23 special wards of Tokyo, Japan. As of 2008, it has an estimated population of 208,371 and a population density of 13,540 persons per km². The total area is 15.11 km²....
which is read as ichi-maru-kyū. (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 .
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.
The numbers 4 and 9 are considered unlucky in Japanese: 4, pronounced shi, is a homophone for ; 9, when pronounced ku, is a homophone for . See tetraphobia
Tetraphobia
Tetraphobia is an aversion to or fear of the number . It is a superstition most common in East Asian regions such as Mainland China, Taiwan, Japan, Korea and Vietnam....
. The number 13 is sometimes considered unlucky, though this is a carryover from Western tradition
Triskaidekaphobia
Triskaidekaphobia is fear of the number ; it is a superstition and related to a specific fear of Friday the 13th, called paraskevidekatriaphobia or friggatriskaidekaphobia.The term was first used by Isador Coriat in Abnormal...
.
In modern Japanese, the digits 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. 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 involving voicing or gemination
Gemination
In phonetics, gemination happens when a spoken consonant is pronounced for an audibly longer period of time than a short consonant. Gemination is distinct from stress and may appear independently of it....
of certain consonants, as typically occurs in Japanese (i.e. rendaku
Rendaku
is a phenomenon in Japanese morphophonology that governs the voicing of the initial consonant of the non-initial portion of a compound or prefixed word...
): e.g. roku "six" and hyaku "hundred" yield roppyaku "six hundred".
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 |
Rendaku
is a phenomenon in Japanese morphophonology that governs the voicing of the initial consonant of the non-initial portion of a compound or prefixed word...
.
Large numbers
Following Chinese tradition, large numbers are created by grouping digits in myriadMyriad
Myriad , "numberlesscountless, infinite", is a classical Greek word for the number 10,000. In modern English, the word refers to an unspecified large quantity.-History and usage:...
s (every 10,000) rather than the Western thousands (1000):
| 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 Western 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, in reading, the digit zero is sometimes pronounced as tobi (飛び) or tonde (飛んで) to indicate the lack of numbers, e.g. yon-sen tobi ni or yon-sen tonde ni can be used 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.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
Japanese units of measurement
' is the traditional Japanese system of measurement. The name shakkanhō originates from the name of two of the units, the shaku, a unit of length, and the kan, a mass measurement.The system is Chinese in origin...
. 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, 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
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, only the formal numbers for one, two, three, and ten are used in legal documents. They 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). 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
Banknotes of the Japanese yen
The banknotes of the Japanese yen are part of the physical form of Japan's currency. The issuance of the yen banknotes began in 1872, two years after the currency was introduced. Throughout its history, the denominations have ranged from 0.05 yen to 10,000 yen.- Before World War II :In 1872, the...
, 1000-yen, 2000-yen, 5000-yen, and 10000-yen, have formal numbers 千, 弐千, 五千, and 壱万 respectively.
Old Japanese
Old JapaneseOld Japanese
is the oldest attested stage of the Japanese language.This stage in the development of Japanese is still actively studied and debated, and key Old Japanese texts, such as the Man'yōshū, remain obscure in places.-Dating:...
shares some vocabulary with later periods, but there are also some unique numbers which are not used any more.
Notes:
- The transcription is based on the phonemePhonemeIn a language or dialect, a phoneme is the smallest segmental unit of sound employed to form meaningful contrasts between utterances....
and is not phonetic. See Old Japanese languageOld Japanese languageis the oldest attested stage of the Japanese language.This stage in the development of Japanese is still actively studied and debated, and key Old Japanese texts, such as the Man'yōshū, remain obscure in places.-Dating:...
for further information. - See Jōdai Tokushu KanazukaiJodai Tokushu Kanazukaiis an archaic kanazukai used to write Japanese during the Nara period. Its primary feature is to distinguish between two groups of syllables as discussed below that later merged together.-Syllables:Following are the syllabic distinctions made in Old Japanese....
for information on subscript notation.
| Number | Reading | Examples | Notes |
|---|---|---|---|
| 1 | hi1to2 | hi1to2hi1 (1 day), hi1to2to2se (1 year) | |
| 2 | huta | hutayo1 (2 nights) | |
| 3 | mi1 | mi1so1 (30) | |
| 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 | ko2ko2no2hashira (9 nobles / gods) | |
| 10 | to2 / to2wo | to2woka (10 days) | |
| 10 | so1 | mi1so1 (30), yo2so1 (40), muso1 (60), yaso (80) | Found only in compound words; not used alone. |
| 20 | hata | hatati (20), hatatari (20 people), hatato2se (20 years) | |
| 50 | i | ika (50 days) | |
| 100 | ho | iho (500), ihoto2se (500 years), ihoyo2 (500 nights), yaho (800), mi1ho (300), muho (600), ko2ko2no2ho (900) | Used for multiple hundreds. Often used to mean many. |
| 100 | mo1mo1 | mo1mo1ka (many days) | Used for non-multiple hundred. Often used to mean many. |
| 1000 | ti | tito2se (1000 years, many years) | Often used to mean many. |
Hand counting
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.External links
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)