one tenth is 1/10, and one quarter is 1/4.
there are a second set of numbers for counting that goes.
1 First
2 Second
3 Third
4 Fourth
5 Fifth
6 Sixth
7 Seventh
8 Eighth
9 Ninth
10 Tenth
and so on
if you say the number one before these numbers, for example "one ninth" then it means if the thing is cut into 9 pieces, this is 1 if those pieces, or 1/9.
And if you say "two ninths" then it means if the thing is cut into 9 pieces, this is 2 of those pieces, or 2/9
"first" and "second" are only used for the order of things, for example the winner of a race comes first, and the person right after them is second.
so we would never say 1/2 as "one second" instead we say "one half" and for 1/4 we either say "one quarter" or "one fourth" both are correct.