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How do Japanese decimal fractions work?

Generally, modern Japanese uses decimal points and numerals, so 0.123 is described as rei ten ichi ni san or zero ten ichi ni san, literally "zero point one two three". In addition to this modern system, Japanese also has two systems of special numerals for decimal fractions.

One system is as follows:

Rōmaji	Kanji	Fraction
bu	分	one tenth; 10^-1
rin	厘	one hundredth; 10^-2
mō	毛	one thousandth; 10^-3
shi	糸	10^-4
kotsu	忽	10^-5

In this system, 0.123 becomes ichibu nirin sanmō (一分二厘三毛).

This is the system used with the traditional system of measurements, Shakkanhō. (See What are the old Japanese units like shaku?) Several of the names are used "as is" to represent a fraction of a shaku.

The other system is 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

In this system, 0.123 becomes ichiwari nibu sanrin (一割二分三厘).

Wari is often used with prices, for example san-wari biki (3割引き) means "30% discount". In baseball, daritsu san-wari hachi-bu kyū-rin (打率3割8分9厘) means "batting average .389"

However, except for wari, these fractional forms are unusual in modern usage. Decimal fractions are typically written with Arabic numerals (1, 2, 3,...) in horizontal writing (yokogaki), preceded by a decimal point, and are read as successive digits, as in Western convention, as in ichi ten ni san for 1.23. Kanji numerals are sometimes also used in vertical writing, tategaki. (See Can Japanese be written right to left? for more on directions of writing in Japanese.) They can be combined with either the traditional system of expressing numerals (42.195 kilometers: gojūni ten ichi kyū go kiromeetoru (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: gojū ten zero yon paasento (五〇・〇四パーセント).

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