(1) OP seems to be confounding "fractions" (rational numbers) and "decimal fractions," i.e. fractions that can be expressed with a poweroften denominator. Not all rational numbers are decimal fractions.
(2) OP also seems to think that invalidating a proof of A automatically proves ~A (notA). It doesn't. (Here, A is "The square root of 2 is irrational.")
OP, of course, did not invalidate the proof. What he actually did was (1).
Expressing the statement that the (positive) square root of 2 is rational as an equation in positive integers p and q,
(*) p^{2} = 2*q^{2}
invites a Euclidean proof that the square root of 2 is not rational, because the equation is impossible.
Euclid also proved a result now known as the Fundamental Theorem of Arithmetic, AKA unique factorization.
The equation (*) violates the Fundamental Theorem, because the left side is divisible by 2 evenly many times, while the right side is divisible by 2 oddly many times.
