My question is about how we form the cases when numbers are made up of multiple parts.

For example:

of one hundred ста

But - if it is "of one hundred and eighty" is this: сто восмидесяти or ста восмидесяти?

Or, again - if it is "of one hundred and seventy-eight" is it сто семьдесять восьми or ста семидесяти восьми?

I.e. is it only the last part which goes into the case (in this case genitive) - or is it every single part of it?

спасибо

Cardinal numerals → every part.
Ordinal numerals → last part only.

3. Even Russians often do mistakes with this. I'm a native Russian and today we have studied this theme in my university. A question was: 1918. Decline it to all cases. No one has been able to answer right))) Just because in real life we rarely use it and most people do mistakes when it happens (and do not realize this).

I just try 1918 again now.
Родительный: Одной тысячи девяти ста восемнадцати
And then I check it in google:
Родительный: Одной тысячи девятисот восемнадцати

I have done the mistake now) This is very hard even for me. Further more, it seems to me that одной тысячи девятьсот восемнадцати sounds better, but it's wrong...

But I don't say that you do not need to learn it. Just bear in mind that in all cases except nominative case Russians will say this numbers wrong in 80% events.

4. Declining numbers in cases you should decline each part according to its own rules.
Examples:
Именительный - Одна тысяча девятьсот восемнадцать; Сто восемьдесят
Родительный - Одной тысячи девятисот восемнадцати; Ста восьмидесяти
Дательный - Одной тысяче девятистам восемнадцати; Ста восьмидесяти
Винительный - Одну тысячу девятьсот восемнадцать; Сто восемьдесят
Творительный - Одной тысячей девятьюстами восемнадцатью; Ста восьмьюдесятью
Предложный - Одной тысяче девятистах восемнадцати; Ста восьмидесяти

5. BTW, «одна тысяча» is used quite rarely. It’s just «тысяча» in most cases.

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