Fractions, Percentages, and Decimals in Japanese

Where number talk breaks down

Most learners meet counters early and assume the number work is done. Then a shop sign says sanwaribiki, a pharmacist says the dose is a third of a tablet, and a colleague reports that sales are up two wari. None of those are counter problems. They are separate patterns with their own word order, and each one appears in ordinary speech far more often than the large numbers beginners drill.

The good news is that there are only four patterns to learn: bun no for fractions, pāsento and wari for proportions, ten for decimals, and bai for multiples. Around them sits a small vocabulary of change and comparison. Learn those together and price tags, weather forecasts and news headlines all open at once.

Fractions put the denominator first

The pattern is denominator plus bun no plus numerator. Sanbun no ichi is one third, and yonbun no san is three quarters. Note that 分 is read bun here, not fun as in minutes or bu as in the discount system below. The number readings stay in their common forms: yon for four, nana for seven, kyū for nine.

A fraction can sit anywhere a number sits. It takes no of its own before a noun, as in sanbun no ichi no ryō, meaning a third of the amount. When you are dividing something between people, add zutsu: sanbun no ichi zutsu means a third each.

Hanbun and the everyday half

Nibun no ichi is mathematically correct but rare in conversation. For a half you say hanbun, and it behaves like a noun: hanbun ni kiru, to cut in half, hanbun dake, only half, hanbun ijō, more than half. The prefix han also attaches to counters you already know, giving ichijikan han for an hour and a half and hangaku for half price.

Hanbunko, with the child-friendly ko ending, is a casual way to say let us go halves and is common between friends and within families. Keep it out of business speech, where hanbun zutsu or the split-bill vocabulary later in this post fits better.

Percentages with pāsento

Pāsento is the everyday word for percent in forecasts, batteries, survey results and science. The sound changes you already know from counters apply: ten, twenty, thirty and so on take the small tsu before the p, giving juppāsento, nijuppāsento and sanjuppāsento. Numbers that end in other digits keep their plain reading, so twenty-five is nijūgo pāsento.

The symbol ％ is read pāsento as well, and a percentage discount printed in digits is usually spoken with biki attached, so a 20％ tag becomes nijuppāsento biki in a staff member's mouth. To ask how big a discount is, say nan pāsento biki desu ka. Note that pāsento is the figure itself, while a rate expressed as a proportion of something takes ritsu, as in the news vocabulary later in this post.

The wari, bu and rin system

Alongside pāsento, Japanese keeps a native decimal system for proportions. Ichiwari is one tenth, so ten percent. Ichibu is one hundredth, so one percent, and ichirin is one thousandth, so a tenth of a percent. The three stack from largest to smallest, which is how a baseball average such as .325 is said: sanwari nibu gorin.

Wari is the one you must own. It appears in discounts, in rough talk about people and results, and in business reporting where niwari sounds more natural than nijuppāsento. Watch the reading of 分 here: it is bu in this system, bun in fractions, and fun in clock minutes. Also remember the fixed expression gobu gobu, meaning fifty-fifty or an even chance.

Because wari counts tenths, converting is a single step: multiply by ten for percent, divide by ten to go back. Hachiwari no hito means eighty percent of people, and the softened hachiwari gurai is the usual way to say most of them without claiming a measured figure.

Reading a sale sign

This is the sentence worth memorising: sanwaribiki means thirty percent off, not thirty percent of the price. The biki comes from hiku, to subtract, so the wari figure is what is taken away. You pay the remaining seventy percent. Learners who read it the other way walk away from a good deal or expect a bargain that is not there.

Retail jargon offers the mirror image. Nanakake, seven times, means you pay seven tenths of the list price, which is the same as sanwaribiki. Hangaku is half price. Zeikomi means the tax is already in the figure and zeinuki means it is not, and staff will often confirm which before you pay.

Decimals with ten

The decimal point is ten, written 点 or as the middle dot ・ in vertical text. Read the whole number normally, say ten, then read each digit after the point on its own. So 3.14 is san ten ichi yon, and 12.05 is jūni ten rei go. Zero is rei in careful speech and zero in casual or technical speech.

Where a counter follows, it usually attaches after the whole expression: ichi ten go bai for one and a half times, ni ten go kiro for two and a half kilos. Temperatures in everyday speech follow the same shape, sanjūnana ten ni do for 37.2 degrees.

Multiples with bai

Bai attaches to a number to make a multiple: nibai twice, sanbai three times, jūbai ten times. On its own, bai already implies double, so ryōkin ga bai ni narimashita means the fee doubled. The question form is nanbai, how many times over.

To describe something as so many times bigger than something else, use A wa B no nibai desu, with no linking the comparison. Adding a measurement noun makes it precise: nibai no hirosa, twice the size, nibai no jikan, twice the time. The opposite direction is hanbun ni naru, to halve.

Increase, decrease and comparison

Numbers rarely stand alone in speech. They arrive attached to a verb of change and a comparison. Fueru and heru are the intransitive pair, meaning something increases or decreases by itself, while fuyasu and herasu mean you increase or reduce it. For prices and rates, agaru and sagaru are more natural than fueru and heru.

Wrap the figure in a hedge unless you are certain of it. Yaku and daitai mean about, gurai softens a round number, and ijō, ika and miman mark more than, no more than, and under. Ni kurabete introduces the thing you are comparing with, and zengo after a figure means give or take.

• 増える fueru and 減る heru: the amount changes on its own
• 増やす fuyasu and 減らす herasu: you change the amount
• 上がる agaru and 下がる sagaru: prices, rates and temperatures
• 約 yaku, だいたい daitai, ぐらい gurai: approximately
• 以上 ijō, 以下 ika, 未満 miman: at least, at most, under
• ～に比べて ni kurabete and ～前後 zengo: compared with, give or take

Statistics in the news

News Japanese leans on ritsu, a rate: shijiritsu for an approval rating, shitsugyōritsu for unemployment, shichōritsu for viewing figures, daritsu for a batting average. These take wa and a figure, often with a verb of movement such as koeru, to exceed, or warikomu, to fall below. Listening for the ritsu word first tells you what the number is measuring before the number arrives.

Splitting the bill

Warikan, from waru, to divide, is the standard word for an even split. The polite offer is warikan ni shimashō ka. To propose a per-person figure, use the amount plus zutsu, and to ask for separate bills at the till say betsubetsu de onegai shimasu, though small restaurants sometimes ask you to settle as one group.