Express "ten" in Russian: difference between десять, десятка, десяток

Question

In terms of expressing ten, what's the difference between десять, десятка and десяток? I understand the first is a numeral and the other two are nouns, but I'm curious in which contexts each are used.

Also, in the sentence Он сыграл в кино десятки ролей, is десятки a declension of десятка or десяток?

Answer 1

Десятка - typically, an informal reference to something numbered 10 (like a bus following route 10) or about a 10 ruble banknote (in the past, when it mattered more) - now it can sometimes informally mean 10 thousand rubles; inform. about sentencing to 10 years of imprisonment (ему дали "десятку").

Десяток - 10 pieces (similar to a dozen eggs etc.), 10 years of age in expressions like "ему уже седьмой десяток" (he's already in his 60's), also about approximate length in time (прошёл/пройдёт десяток лет - один или более десятков); mathematically, десятки (plural) - the position of tens in a number.

P.S. In "Он сыграл в кино десятки ролей" десятки из the plural of десяток in accusative case.

Answer 2

Also, in the sentence Он сыграл в кино десятки ролей, is десятки a declension of десятка or десяток?

this is a declined десяток

десятки is never meant in a literal sense of quantity but just used to indicate great amount within certain limits, in this case under 100
in this usage, as Alex_ander has noted, it's better to be understood as idiomatic dozens

likewise cотни, тысячи, десятки тысяч and so on

at the same time десяток and nouns just listed can indicate a precise number if appended by a numeral

Он сыграл в кино два десятка ролей

or express uncertainty about the accuracy of the number (quantity) if followed by one (this is a case of a more general syntactic rule)

Он сыграл в кино десятка два ролей

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so in an attempt to summarize it might be said that десятка (and any other numeral cognate noun ending with -ка such as тройка, семёрка, двадцатка, пятидесятка and so on) can be applied to something solid and indivisible, whereas десяток - to a set of separate items of one kind

the difference may be exemplified with the following sentence

Я купил десяток (штук) десяток = Я купил десять (штук) десяток

where the 2nd десятка means an item numbered 10, for example a spool of sewing thread size 10, and so the entire sentence means I've bought ten items of the (number) 10

Answer 3

ДЕСЯТКА noun (colloquial ) feminine. 1.The name of the number "ten".

2.colloquial. The name of means of transport (a bus, a tram ) which has number 10

Какой автобус тут ходит?--Десятка.

3. Bull's-eye (sports )--a black central circle --десятка,

   An idiom попасть в десятку--To hit on the right nail.

4.A ten--rouble coin--десятка.

5. A card The ten of spades--десятка пик,the ten of hearts-- десятка червей.

ДЕСЯТОК A noun, masculine.

1. Ten things ( like a dozen )

   Десяток пирожных.

   2.Ten years of age.

   Ему пошёл шестой десяток.

3.A group of ten people.

Десяток ребят.

4.in mathematics, tens --тысячи, сотни, десятки, единицы.

5 a score of десятка два людей

Idioms

Не робкого десятка --he is brave. Добрый десяток лет.--over a decade.