Numerals are cardinal (один - one, десять - ten), ordinal (первый - first, десятый - tenth), collective (двое - two, оба - both) and fractional (полтора рубля - one and a half roubles, две трети - two thirds). Also, they are simple (one root - сто), complex (several roots - двадцать) and compound (several words - сто двадцать первый).

Spelling of numerals:

Double consonantsЬ in the words in Nominative and Accusative casesЬ never stands in the middleЬ in the end
Пятьдесят, восемьсот,
50 - 80, 500 - 900
Пятнадцать, шестнадцать, семнадцать, восемнадцать, девятнадцать5 - 20/30 Пять, десять, двадцать, тридцать

In everyday life, numerals are used to talk about time, money, age, or temperature, being widely used far beyond some technical fields. If you hear an expression like восемь двадцать (eight twenty), most obviously they are talking about the price ($8.20) or time (8:20).

In Russian, we pronounce 1945 like ‘тысяча девятьсот сорок пять’, while the English is ‘nineteen forty-five’.

Cardinal numerals define the number of objects.

They vary by case and do not have gender (except for один, два) or number (except for один):

Один билет, два билета, много билетов - one ticket, two tickets, many tickets - masculine
Одна роза, две розы, много роз - one rose, two roses, many roses - feminine
но облако, два облака, много облаков - one cloud, two clouds, many clouds - neuter

The others agree with the Genitive case of the following noun, e.g. два (чего?) билета, две (чего?) розы.

Ordinal numerals are the following:

1 - первый
2 - второй
3 - третий

30 - тридцатый
100 - сотый
1000 - тысячный
1 000 000 - миллионный

They change their form depending on the gender, number and case:

Первая скрипка
Вторые дети
[Нет] сотого покупателя
В тридцатые годы

Remember three numerals in Russian obtain two forms when they change by case. They are 40, 90 and 100:

Nominative case40 сорок, 90 девяносто, 100 сто
The rest of cases40 сорока, 90 девяноста, 100 ста.

When you face difficulties declining the compound numerals like триста тридцать третий, remember to decline every separate number (G.c. - трехсот тридцати трех, D.c. - тремстам тридцати трем etc).