# Japanese number system

The Japanese number system is a decimal system and, like the Korean one , is largely a borrowing of the Chinese numerals . In addition to these Sino-Japanese numerals, old Japanese numerals are also used. In everyday life , Arabic numerals are used for horizontally written numbers up to around five digits, as well as in mathematics .

A special feature in Japanese is the use of counting unit words and different naming of the numbers depending on the form of representation and depending on the objects being counted. In addition, the place value system is not grouped in thousands , but in myriads , so there are separate numerals for the numbers 10,000 and 100,000,000 (the square of 10,000), but none for million or billion .

## Base numbering

There are two ways of writing numbers in Japanese: in Arabic numerals (1, 2, 3) or in Chinese numerals ( , , ). The Arabic numerals are often used in horizontal writing, the Chinese numerals are often used in vertical writing and on official documents.

0 * zero ( ゼ ロ ) れ い rei -
1 ichi い ち ichi ひ と ( ) hito (tsu)
2 ni ni , ji ふ た ( ) futa (tsu)
3 san さ ん san ( っ つ ) mi (ttsu)
4th yon ( よ ん ) shi ( っ つ ) yo (ttsu)
5 go go い つ ( ) itsu (tsu)
6th roku ろ く roku ( っ つ ) mu (ttsu)
7th nana ( な な ) し ち shichi な な ( ) nana (tsu)
8th hachi は ち hachi ( っ つ ) ya (ttsu)
9 kyū き ゅ う kyū , ku こ こ の ( ) kokono (tsu)
10 じ ゅ う と お
20th 二十 niju に じ ゅ う ni-jū は た ( ) hata (chi)
100 hyaku ひ ゃ く hyaku ( も も momo )
1,000 sen せ ん sen ( chi )
10,000 ** man ま ん man ( よ ろ ず yorozu )
see section powers of ten
* is also pronounced as a digit maru , which means "circle". A well-known example is the Shibuya 109 department store , pronounced ichi maru kyū .
**From 10,000 the number names are no longer used alone, but only combined, i.e. H. while 1, 10 and 100 are spoken and written as ichi ( ), ( ) and hyaku ( ), from 10,000 it is ichiman ( 一 万 ) instead of just one , ichioku ( 一 億 ) instead of just oku for 100,000. 000 etc. 1000 is a borderline case where both sen ( ) and issen ( 一千 ) are possible. This is similar to German, where smaller number names are only "Eins" and "Zehn", at 100 and 1000 both "Hundred" and "Einhund" or "Tausend" and "Eintausend" are possible, but usually only for larger ones Compositions like "one million" can be used for 1,000,000.

For numbers such as B. the passing on of telephone numbers, the single digits are often pronounced long, i. H. ni like nii , shi like shii and go like .

### Composite numbers

#### Modern Japanese

As in Chinese, compound numbers are formed as multiplicative for the individual digits and additive for the combination of different digits. In contrast to Chinese, empty spaces (i.e. the number zero ) are left out. If a 1 appears as a multiplier, this is usually also left out.

multiplicative composition
30th 三十 san-jū
400 四百 yon-hyaku
50,000 五万 go-man
31 三十 一 san-jū-ichi
452 四百 五十 二 yon-hyaku-go-jū-ni
Omission of zeros and ones
111 百 十一 hyaku-jū-ichi
2006 二千 六 ni-sen-roku
50.020 五万 二十 go-man-ni-jū

Due to phonological phenomena of the Japanese language such as rendaku , in which unvoiced consonants become voiced, and gemination , the following linguistic peculiarities result:

× 1 2 3 4th 5 6th 7th 8th 9 10 100 1000
100 hyaku nihyaku sanbyaku yonhyaku gohyaku roppyaku nanahyaku happyaku kyūhyaku
1000 (is) sen nise sanzen yonsen gosen rokusen noses to hate kyūsen
1,000,000,000,000 itchō nichō sanchō yonchō gochō rokuchō nanachō hatchō kyūchō jutchō hyakuchō issenchō
10,000,000,000,000,000 ikkei nikei sankei yonkei gokei rokkei nanakei hakkei kyūkei jukkei hyakkei issenkei

#### Old Japanese

Before the introduction of the Chinese-influenced system, the Kun reading was used throughout. The units place received the suffix -tsu (historical: / tu /), the tens place -so , the hundreds place -o (historical: / po /), the thousands place -chi (historical: / ti /) and the tens place -yorozu (historical : / yorodu /). Exceptions are the numbers from 10 to 19, where the word (historical: / towo /) was used for 10 , and 20-29 where hatachi (historical: / patati /) was used. The individual places were partially marked by the word amari .

In Nihonshoki there is the number "1,792,470 years" ( 一百 七十 九萬 二千 四百 七十 餘 歲 ) which is glossed as follows :

 一百 七十 九萬 二千 四百 七十 餘 歲 モ ヽ ヨ ロ ヅ ト セ ア マ リ ナ ヽ ヨ ロ ヅ ト セ ア マ リ コ ヽ ノ ヨ ロ ヅ ト セ ア マ リ フ タ チ ト セ ア マ リ ヨ ホ ト セ ア マ リ ナ ヽ ソ ト セ ア マ リ ト シ momo yorodu tose amari nanaso yorodu tose amari kokono yorodu tose amari putati tose amari yopo tose amari nanaso roar amari toshi 100 10,000 years and 70 10,000 years and 9 10,000 years and 2000 Years and 400 Years and 70 Years and Years

The composite and higher numbers were therefore spoken as follows:

number historical pronunciation modern pronunciation meaning number historical pronunciation number hist. pronunciation number hist. pronunciation
10 towo 10 20th patati 100 momo 1000 ti
11 towo amari pito to amari hito 10 + 1 21st patati amari pito
12 towo amari puta tō amari futa 10 + 2 ... 200 * putapo 2000 putati
13 towo amari mi tō amari mi 10 + 3 30th miso 300 mipo 3000 * miti
14th towo amari yo tō amari yo 10 + 4 40 yoso 400 yopo 4000 * yoti
15th towo amari itu tō amari itsu 10 + 5 50 iso 500 ipo 5000 * iti
16 towo amari mu tō amari mu 10 + 6 60 muso 600 * mupo 6000 * muti
17th towo amari nana to amari nana 10 + 7 70 nanaso 700 * nanapo 7000 * nanati
18th towo amari ya tō amari ya 10 + 8 80 yaso 800 yapo 8000 yati
19th towo amari kokono tō amari kokono 10 + 9 90 kokonoso 900 * kokonopo 9000 * kokonoti

Note: In later language levels, possibly towards the end of Old Japanese, today's / h / was spoken as * [ɸ].

This pronunciation has survived in a few words. So “20 years old” ( 二十 歳 ) can be read both nijussai and hatachi . The “last day of a month” ( 晦 日 ) can be read regularly kaijitsu , but also misoka , the latter being from Old Japanese for “30. Day “comes from.

### Powers of ten

As in the conventional decimal number system, Japanese have their own number names to denote major and minor powers of ten . For large numbers ( 大数 , taisū ) the number name changes in myriad steps , i.e. in four powers of ten, for small numbers ( 少数 , shōsū ) in steps of ten , i.e. with each change of position. The names come to a large extent from the Buddhist theory of numbers and were already used in the early Middle Ages. The very large potencies, in particular, had different values ​​over time; the number name goku ( ) is assigned values ​​corresponding to 10 14 , 10 44 or 10 80 in various sources . Even today, the very large number names from 10 52 are assigned values ​​that can be 10,000 times greater than the official assignments.

10 1 ten
10 2 Hundred hyaku
10 3 thousand sen
10 4 Ten thousand man
10 8 100 million oku
10 12 1 trillion chō
10 16 10 quadrillion kei , kyō
10 20 100 trillion gai
10 24 1 quadrillion shi , jo
10 32 100 quintillion
10 36 1 sextillion can
10 40 10 sextillion be
10 44 100 septillion sai
10 48 1 octillion goku
10 52 10 octillions 恒河沙 gōgasha
10 56 100 nonillion 阿僧祇 asogi
10 60 1 decillion 那 由 他 nayuta
10 64 10 decillion 不可思議 fukashigi
10 68 100 undezillion 無量 大数 muryōtaisū
10 −1 bu
10 −2 , rin , ri
10 −3 , ,
10 −4 , shi
10 −5 kotsu
10 −6 bi
10 −7 sen
10 −8 sha
10 −9 jin
10 -10 ai
10 −11 byō
10 −12 baku
10 −13 模糊 moko
10 -14 逡巡 shunju
10 -15 須臾 shuyu
10 −16 瞬息 shunsoku
10 −17 弾 指 danshi
10 −18 刹那 setsuna
10 −19 六 徳 rittoku
10 −20 虚空 goku
10 −21 清浄 seijō
10 −22 阿 頼 耶 araya
10 −23 菴 摩羅 ammara
10 −24 涅槃 寂静 nehanjakujō

The Buddhist origin is particularly evident in the last, exceptionally long number names. The name for the value 10 52 kōgasha ( 恒河沙 ) is derived from the Buddhist term for the number of grains of sand in the river Ganges , which was regarded as the epitome of the infinity of the world. The word fukashigi ( 不可思議 ) still denotes fushigi ( 不 思議 ) in a shortened form, something wondrous, strange or puzzling. The last number word muryōtaisū ( 無量 大数 ) is the term for an “immeasurably large number”.

The number names for the small numbers are also rarely used, but are still used in certain areas today. In the sporting sector, for example, the hit rates of a batsman in baseball or in advertising the discount for an action are shown with these numbers. Depending on the context, however, there may be a shift by a factor of 10, so the designation 2 分 3 厘 ( ni-bu san-rin ) can mean either the number 0.23 or 0.023. This is done by shifting the number names when introducing the designation wari ( ) for the first decimal place. For clarity, the following table lists the first 4 number names using this designation:

 number character reading 10 −1 10 −2 10 −3 10 −4 割 分 厘 毛 wari bu rin mō

### Fractions

In the case of common fractions , the denominator is mentioned first and then the numerator:

Three-quarters (3/4): 四分 の 三 ( yon bun no san , literally: "four parts, of which 3")

Decimal fractions are usually represented with Arabic numerals and a point (pronounced ten or comma ) as a decimal separator . In the case of vertical notation or the use of the Chinese numerals that are also possible, the center point is used:

3.14 or

( san ten ichi yon )

## Daiji (bank numbers)

In Japanese finance, so-called Daiji ( 大字 ) are used instead of the Kanji , , , , 万 in order to increase the security against forgery in handwritten documents. Without this, eines 億 円 (100,000,000 yen) could be formed from Str 円 (1,000,000,000 yen) by adding a single dash . There are also no longer commonly used Daiji.

These are also used on Japanese banknotes.

Daiji (current) Daiji (obsolete) Daiji (unofficial variants)
1
2 貮 、 貳 弍, 贰, 両, 兩, 两
3 弎, 叁, 叄, ?
4th
5
6th
7th 柒 、 漆
8th
9
10
20th 廿 弐 拾, 貳拾 卄, 念
30th 参 拾
40 四 拾
100 陌 、 佰
1000 阡 、 仟
10,000

## Japanese number mysticism

The numbers 4 and 9 are unlucky numbers in Japanese: 4, pronounced shi , is a homophone for "death"; 9, when pronounced ku , is a homophone for "suffering". The number 13 is also sometimes understood as an unlucky number, although it was adopted from western culture ( Friday the 13th )

In modern Japanese, the Kun reading is only used for single-digit number representations and day-of-month names, even if the On reading is used instead in many contexts. Fractions are made through combination.

## Count words

Different types of objects and abstract terms are each assigned one of the 100 or so counting unit words . It is appended to the number and often supports reading comprehension. An equivalent in German is about Blatt in “50 Blatt Papier”. The assignment of terms and unit words is often based on the shape and size of an object, but less frequently used assignments also pose problems for native speakers. Depending on the unit word, certain numbers are pronounced irregularly.

Example: one bottle, two bottles, three bottles
bin ippon, nihon, sanbon ( び ん １ 本 、 ２ 本 、 ３ 本 )

When counting with unit words, the On reading, i.e. the Sino-Japanese counting method, is almost always used (there are also cases in which it is mixed, e.g. people 1 人 、 2 人 、 3 人 hitori, futari, sannin ). If you only count things with the Kun reading, i.e. in Japanese, you don't need any numbering unit words. However, this only goes up to the number ten.

## Numbers

The old Japanese counting unit words from "1" to "10" are used for numbers without a counting unit word, as well as in connection with a few specific counting unit words. Alone they receive the Okurigana ( -tsu ) up to “9” .

The pronunciation changes described above ( rendaku and gemination) also take place.

Example: "4" and "day" result in "the 4th day" [of the month]
yotsu + ka >> yokka ( 四日 )

## Spelling with Arabic numbers

The structure of multi-digit number representations take over the Sino-Japanese numerals. Kanji are often written vertically for numerals, with horizontal writing the characters for 1000 ( ), 10,000 ( ) and the multiple of the latter usually take on the role of a separator between the Latin numerals ( eisūji ).

Example: "19800 Yen" ichiman-kyūsen-happyaku En ( 1 万 9 千 800 円 )

When writing with Arabic numerals, the point is sometimes used as a separator of the myriad and not the thousand, which can easily lead to errors in translation.

Example: German 200,000,000 yen equals Japanese 2.0000.0000