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Basic numbering in JapaneseThere are two ways of writing the numbers in Japanese, in Hindu-Arabic numerals (1, 2, 3) or in Chinese numerals (一, ニ, 三). The Hindu-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" 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 which is read as "ichi-maru-kyū". This usage of "maru" for numerical 0 is similar to reading numeral 0 in English as "oh". Etymologically, it derives from 丸 or 円 (both "maru"). However, as a number, it is only written as 0 or 零. 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). The number 13 is sometimes considered unlucky, though this is a carryover from Western tradition. In modern Japanese, the kun readings are only used for single digit numbers and day-of-month names, although in many contexts the on readings will be used instead. Intermediate numbers are made by combining these elements:
In large numbers, elements are combined from largest to smallest, and zeros are implied.
Powers of 10Large numbersFollowing Chinese tradition, large numbers are created by grouping digits in myriads (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 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 302 is 三百二. In contrast, Chinese requires the use of 零 wherever a zero appears, e.g. 三百零二 for 302. Decimal fractionsJapanese 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:
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 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). Formal numbersLike 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. Some formal numbers are obsolete and not used in legal documents today. Those that remain 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). The digit 1 is explicitely written like 壱百壱拾 for 110, as opposed to 百十 in common writing. Formal numbers:
Old JapaneseOld Japanese shares some vocabulary with later periods, but there are also some unique numbers which are not used any more. Notes:
See also
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