How to ask the position(?) of a president (like 10th) of a country, correctly?
Probably this is the first question on this particular issue here on ELL, but it's been asked many times before on ELU. That link is to the one kept open while duplicates are closed (about once a month!).
As the answers there will show, there isn't any "natural" way to succinctly phrase such a question in English. Informally, people sometimes ask things like
but they're not at all standard. The best I can think of that remains strictly "grammatical" is...
...but I don't recommend learners bothering with that either, since not all native speakers would even understand you. Although it's not really "correct", most people would probably just ask something like...
"What number president is Obama?"
I don't particularly like the way this sentence sounds, but I think it's the clearest way to ask your question without being over-elaborate:
What number president was Taft?
So I suggest you say that. But since I don't really like the sound of it, I'll discuss a few other ways to say the same thing:
I like this sentence much better, but it's pretty ambiguous:
Which president was Taft?
. . . so we could probably clarify it a bit. In informal speech, I might say the following:
Which president was Taft, like the thirtieth? Thirty-first?
Which president was Taft? For example, was he the thirtieth president?
Since I gave examples of answers, it's clear what I meant.
You can, of course, spell out exactly what you mean. I avoided doing so because it's difficult to do so concisely. We can write the following sentence, which is precise and acceptable:
In the chronological sequence of Presidents of the United States, which position did Taft occupy?
. . . but it sounds unwieldy to me.
A simple way to ask this kind of question and a way that many speakers do opt for, is with "How many".
How many American presidents (did we have|were there|came) before Obama?
-- He's the 44th president.
How many people were ahead of you in the customer service phone queue?
--I'm third in line.
How many times has he been absent?
--This is his fourth absence.
If you need more precision than that, then you're probably writing or speaking in a specialized domain where unwieldiness plays second-fiddle to precision:
In which offset of the array was the string value found?
What is the item's position in the job queue?