Answer is: the percent ionization of weak acid is 0.266%.
Chemical reaction: HA(aq) ⇄ H⁺(aq) + A⁻(aq).
Ka(HA) = 7.1·10⁻⁷.
c(HA) = 0.10 M.
[H⁺] = [A⁻] = x; equilibrium concentration.
[HA] = 0.10 M - x.
Ka = [H⁺] · [A⁻] / [HA].
0,00000071 = x² / 0.1 M - x.
Solve quadratic equation: x = 0.000266 M.
α = 0.000266 ÷ 0.1 M · 100% = 0.266%.