I checked and it says "Numerical adjectives include all numbers; however, only cardinal numbers are determiners, because fractions and ordinal numbers can be used with articles."
"Trois" means three, whereas "troisieme" means third. There's a big difference between three and third.
"Three" is just a whole number between two and four. "Third" is an adjective used to state that something is on position number three in any given list or sequential order.
There is a "quatrieme" (not quartieme), and a "cinquieme" (not cinqieme). The list just goes on with "sixieme", "septieme", "huitieme", and so on . Basically, by adding an -ieme after a number, you will get its ordinal (i.e. second, third, fourth, fifth, etc) form.
The only exception is that "first" is written as "premiere" and not "unieme" or "uneieme".