Pi isn’t a fraction – it’s an irrational number, i.e. a number with no fractional form in integer bases. Furthermore, it’s a transendental number, meaning it’s never a solution to f(x) = 0, where f(x) is a non-zero finite-degree polynomial expression with rational coefficients. That’s like, literally part of the definition. They cannot be compared to rational numbers like integer ratios/fractions.

Since |r|<1 => ∑[n=1, ∞] arⁿ = ar/(1-r), and 0.999… is that sum with a = 9 and r = 1/10 (visually, 0.999… = 9(0.1) + 9(0.01) + 9(0.001) + …), it’s easy to see after plugging in, 0.999… = 9(1/10) / (1 - 1/10) = 0.9/0.9 = 1). This was a proof in Euler’s Elements of Algebra.