Zero, Decimals, Fractions, and Math

Whole numbers are only half of everyday counting. The moment you talk about temperatures, prices, statistics, recipes, or a phone number, you need zero, decimals, fractions, percentages, and the four arithmetic operations. Japanese handles each of these differently from English — sometimes trivially, sometimes in a way that quietly reverses the word order you're used to. This page pulls all of it together, and singles out the one thing that catches almost every English speaker: fractions are said denominator first.

Four ways to say zero

English gets by with one core word ("zero," plus casual "oh" and "nought"). Japanese has four, and they are not interchangeable — each belongs to a different situation.

れい (零) is the mathematically precise zero. You use it for decimals (〇点五 rei-ten-go, 0.5), for temperature (零度 rei-do, zero degrees), and in careful, formal readings.

ゼロ is the casual, spoken zero — the one you'll hear most in conversation, and the standard for sports scores.

まる (literally "circle," the same 〇 you draw on a correct answer) is how you read a lone zero embedded in a sequence of digits — room numbers, phone numbers, flight numbers — where the digits are spoken one at a time.

The bare 〇 also appears as a written positional zero, mainly in vertical text and newspaper-style dates: 二〇二六年 for the year 2026 (still read ni-sen-ni-jū-roku-nen, the full number — 〇 is just the vertical spelling of the "0" slot).

Decimals: 点 plus digit-by-digit

The decimal point is the word 点 (てん) ten, "point." Everything before the point is a normal number; everything after the point is read one digit at a time — exactly like English "three point one four," never "three point fourteen."

Notice 三点一四 is san-ten-ichi-yon, digit by digit — not san-ten-jūyon. The number to the left of 点 obeys all the normal rules (三 = three), but to the right you simply list the digits: 一, 四.

When there's no whole part, the zero is spoken: 〇点八 rei-ten-hachi (0.8), 〇点〇五 rei-ten-rei-go (0.05). English often drops the leading zero ("point eight"); Japanese usually keeps 〇 in careful speech.

Fractions: denominator FIRST

Here is the single most important — and most counter-intuitive — point on this page. A fraction is built with 分の (ぶんの) bun no, and the pieces come in the opposite order from English:

[denominator] 分の [numerator]

三分の一 is literally "of three parts, one" → one third. You name the size of the pieces first (into how many parts the whole is divided), then how many you take. English says the numerator first ("one third"); Japanese says the denominator first ("three-parts-of, one").

二分の一 = ni-bun no ichi = "of two parts, one" = one half. Read it left to right and force yourself to think "denominator, then numerator" every single time until it's automatic.

四分の三 = yon-bun no san = "of four parts, three" = three quarters. If you translated word-for-word you'd get "four-of-three," which is why literal translation is a trap here.

For "half" in everyday, non-mathematical speech, Japanese usually prefers the plain noun 半分 (はんぶん) hanbun over 二分の一:

Use 半分 when you just mean "half of it" in conversation; use 二分の一 when you're being mathematical (probabilities, ratios, textbook problems).

That example ties the whole page together: the fraction 二分の一, its decimal equivalent 〇点五, and 点 all in one breath.

Percentages: パーセント and the native 割

Japanese has two systems for proportions, and you need both.

パーセント pāsento (percent) is the borrowed system, identical to English in meaning: 五十パーセント go-jup-pāsento = 50%. The question word is 何パーセント nan-pāsento ("what percent").

割 (わり) wari is the native system, and it counts in tenths: one 割 = 10%. So 五割 = 50%, 八割 = 80%, and 十割 jū-wari = 100%. This is where English speakers stumble — 割 looks like a small number but each unit is worth ten percentage points.

五割引き go-wari-biki = "five-tenths off" = 50% off. 割引 (わりびき) waribiki is the everyday word for "discount," and you'll see it constantly on price tags: 二割引 (20% off), 三割引 (30% off).

For real precision, 割 has sub-units — 分 (ぶ) bu = 1% and 厘 (りん) rin = 0.1% — most famous from baseball batting averages: a .325 hitter bats 三割二分五厘 san-wari ni-bu go-rin. This is (specialized) — you'll meet it in sports and finance, not casual chat, but it's worth recognizing so you don't misread 分 here as "minutes."

The four operations

Arithmetic uses four everyday verbs. In spoken sums, the "equals" is usually the particle は wa or the loanword イコール ikōru.

These verbs are alive outside pure arithmetic. 割る in particular does real conversational work whenever a bill gets split:

For signed numbers and temperatures, "plus/minus" become the loanwords プラス purasu and マイナス mainasu: マイナス五度 (minus five degrees), プラスマイナスゼロ ("plus-minus zero," i.e. it evens out).

Common mistakes

The flagship error: mapping English "one third" straight onto 一分の三. In 分の, the number touching 分 is the denominator, so it must come first. "One third" is 三分の一.

After 点, read each digit separately: 一四, not 十四. There is no "point fourteen" in either language.

割 counts tenths, so every unit is worth 10%. 五割 is 50%, not 5%. Multiply by ten.

れい is the mathematical zero (decimals, temperatures). For a digit read aloud inside a phone or room number, use ゼロ or まる.

Key takeaways

• Zero has four faces: 零 rei (math, decimals, temperature), ゼロ (casual, scores), まる (a zero inside a digit string), and the written 〇 (vertical/date zero).
• Decimals use 点 ten, and every digit after the point is read individually: 三点一四 = san-ten-ichi-yon.
• Fractions are denominator-first: [denominator]分の[numerator], so 三分の一 = one third. For casual "half," use 半分.
• Percentages: パーセント is 1-for-1 with English; the native 割 counts in tenths (五割 = 50%, 十割 = 100%).
• Arithmetic: 足す (+), 引く (−), かける (×), 割る (÷), with は or イコール for "equals," and プラス/マイナス for signed numbers.

For where these figures sit in the wider number system, see Two Number Systems and Large Numbers; to say "the third" rather than "three," continue to Ordinal Numbers.