'The one hundredth is mine' is perfect English (in England at least) too. We can put in or omit the one. We can say a hundred brisks or one hundred bricks but to say a hundredth brick doesn't seem right so I'd say the nearest translation to the Romanian is to include the one in the answer as they have included the specific indefinite singular article. Going back to the duolingo English translation it is not quite as good as 'one hundredth' as if the hundredth is mine I could mean the fraction, whereas if we used one then we would have to leave out the 'the' and have just 'a' or 'one hundredth is mine'. TO stress ordinal over fraction we might also say 'the hundredth one is mine.'
Perfect English, yes, but for the life of me I can't see why it's "better" English. It's certainly not what I (a BrE speaker) would say, and it's a lot less common:
I think we usually say, for example, "for the hundredth time"