Fractions, Decimals, and Половина

Once you can count whole things, the next step is counting parts of them — a half, two thirds, three point one four. Russian handles this with three separate systems that learners often blur together: ordinary fractions (built from a cardinal over a feminine ordinal), the family of words for "half" (the noun полови́на, the prefix пол-, and the irregular numeral полтора́), and decimals, which Russian reads aloud quite differently from English and — famously — punctuates with a comma, not a point. Each has its own grammar; the unifying thread is that fractions and "half" all reach for the genitive of whatever is being divided.

Ordinary fractions: cardinal over ordinal

A Russian fraction is read as [cardinal numerator] [ordinal denominator], and the denominator is an ordinal adjective in the feminine, because it silently agrees with the noun до́ля or часть ("part", both feminine). So 1/3 is одна́ тре́тья — literally "one third [part]". The numerator then governs the denominator just as numbers govern nouns: after одна́ the denominator is feminine nominative singular, but after две, три, четы́ре and up it goes into the genitive plural (the -ых form).

The noun that the whole fraction refers to stands in the genitive singular: две тре́тьих населе́ния ("two thirds of the population"). The verb after a fraction is usually singular/neuter.

Полови́на — the noun for "half"

The everyday word for a half is the feminine noun полови́на. Being a noun, it takes the thing halved in the genitive: полови́на я́блока ("half an apple"), полови́на гру́ппы ("half the group"). It declines normally (полови́ны, полови́не…).

The prefix пол- / полу-

For fixed, common half-quantities, Russian fuses пол- ("half") onto the front of a noun in the genitive: полчаса́ ("half an hour", from час), полго́да ("half a year"), полдня́ ("half a day"), полме́тра, полкило́. The variant полу- forms more abstract or compound words: полуфина́л ("semifinal"), полусо́н ("half-sleep"). In the oblique cases of these пол- words, the front often shifts to полу- (получа́са, but в течение получа́са).

Полтора́ / полторы́ — the irregular 1½

"One and a half" is a single irregular numeral, полтора́ — and it has a gender split: полтора́ with masculine and neuter nouns, полторы́ with feminine ones. Like 2–4, it governs the genitive singular of the noun: полтора́ часа́ ("an hour and a half"), полторы́ неде́ли ("a week and a half"), полтора́ го́да ("a year and a half"). In the oblique cases there is just one fused form, полу́тора, for all genders.

Decimals: read with це́лых and written with a comma

Two things shock English speakers here. First, Russian writes the decimal separator as a comma, never a period: 3,14, not 3.14. Second, you read a decimal as [whole-part] це́лых [fractional-part] [denominator-ordinal] — це́лых being the genitive plural of це́лая ("a whole [unit]"). The fractional part is named by its place value: tenths (деся́тых), hundredths (со́тых), thousandths (ты́сячных).

Note the feminine две / одна́ before це́лых — це́лая is feminine, so the numerator agrees with it.

The distinguishing insight

The thread tying all of this together is that Russian treats a part as a thing in its own right that then takes a genitive complement, the same machinery as counting. A fraction's denominator is secretly an adjective modifying до́ля ("part"); полови́на is just a noun; це́лая ("a whole") is a noun the decimal counts in tenths and hundredths. So "half of the apple", "two thirds of the population", and "three point one four" are all, underneath, [quantity] of [genitive] — exactly the partitive logic of the genitive after quantity. The comma vs point difference is the one purely orthographic trap, but it is a real factual error to get wrong: a Russian reader sees "3.14" as broken.

Common Mistakes

Key Takeaways

• Fractions = cardinal numerator + feminine ordinal denominator (agreeing with до́ля 'part'): одна́ втора́я, одна́ тре́тья; after две/три/… the denominator goes genitive plural — две тре́тьих, три четвёртых. The divided noun is genitive singular.
• Полови́на is a noun for "half" and takes the genitive (полови́на я́блока). The prefix пол-/полу- forms fixed halves (полчаса́, полго́да, полдня́).
• Полтора́ / полторы́ (1½) splits by gender (masc./neut. полтора́, fem. полторы́) and takes the genitive singular (полтора́ часа́, полторы́ неде́ли); oblique form полу́тора. Полтора́ста = 150.
• Decimals use a comma (3,14) and are read with це́лых plus a place-value ordinal: три це́лых четы́рнадцать со́тых. Never "three point fourteen".