# Japanese numerals

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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 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.

(Some numbers have multiple names.)

0 / 〇* zero rei / れい -
1 ichi ichi / いち hito(tsu) / ひと(つ)
2 ni ni, ji / に, じ futa(tsu) / ふた(つ)
3 san san / さん mi(ttsu) / み(っつ)
4 yon shi / し yon, yo(ttsu) / よん、よ(っつ)
5 go go / ご itsu(tsu) / いつ(つ)
6 roku roku / ろく mu(ttsu) / む(っつ)
7 nana shichi / しち nana(tsu) / なな(つ)
8 hachi hachi / はち ya(ttsu) / や(っつ)
9 kyū kyū, ku / きゅう, く kokono(tsu) / ここの(つ)
10 jū / じゅう tō / とお
20 二十 ni-jū ni-jū / にじゅう hata(chi) / はた(ち)
30 三十 san-jū san-jū / さんじゅう miso / みそ
100 hyaku hyaku / ひゃく (momo / もも)
1,000 sen sen / せん (chi / ち)
10,000 man man / まん (yorozu / よろず)
100,000,000 oku oku / おく -
1,000,000,000,000 chō chō / ちょう -

* The special reading maru 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. 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 ( ?).

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 modern Japanese, the digits are called with 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, but they are a minor detail.

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

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

* Hyaku becomes byaku due to rendaku.

## 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 (1000):

 Rank Character Reading 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 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 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 letter 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 Character Reading 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 10-10 分 厘 毛 糸 忽 微 繊 沙 塵 埃 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 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 Character Reading 10-1 10-2 10-3 10-4 10-5 割 分 厘 毛 糸 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

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. Today, only the formal numbers for one, two, three, and ten are used in legal documents[1][2][3][4]. 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
2
3
4
5
6
7 柒, 漆
8
9
10
100
1000 阡, 仟
10000 万, 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.

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.

## References

1. ^ 大正十一年大蔵省令第四十三号 (会計法規ニ基ク出納計算ノ数字及記載事項ノ訂正ニ関スル件) 第一条: 会計法規ニ基ク出納計算ニ関スル諸書類帳簿ニ記載スル金額其ノ他ノ数量ニシテ「一」、「二」、「三」、「十」、「廿」、「卅」ノ数字ハ「壱」、「弐」、「参」、「拾」、「弐拾」、「参拾」ノ字体ヲ用ユヘシ但横書ヲ為ストキハ「アラビア」数字ヲ用ユルコトヲ得
2. ^ 戸籍法施行規則 第三十一条 2: 年月日を記載するには、壱、弐、参、拾の文字を用いなければならない。
3. ^ 小切手振出等事務取扱規程 附則 (昭和四〇年四月一日大蔵省令第二〇号) 2: 小切手の券面金額は、当分の間、所定の金額記載欄に、漢数字により表示することができる。この場合においては、「一」、「二」、「三」及び「十」の字体は、それぞれ「壱」、「弐」、「参」及び「拾」の漢字を用い、かつ、所定の金額記載欄の上方余白に当該金額記載欄に記載の金額と同額をアラビア数字で副記しなければならない。
4. ^ 商業登記規則 第四十八条 2: 金銭その他の物の数量、年月日及び番号を記載するには、「壱、弐、参、拾」の文字を用いなければならない。ただし、横書きをするときは、アラビヤ数字を用いることができる。