At equilibrium $\left[H^{+}=A^{-}\right]$

$K_{a} =\frac{\left[H^{+}\right]\left[A^{-}\right]}{[H A]}=\frac{\left[H^{+}\right]^{2}}{[H A]}$

$\left[H^{+}\right]=\sqrt{K_{a}[H A]} =\sqrt{1 \times 10^{-5} \times 0.1}$

$= \sqrt{1 \times 10^{-6}}=1 \times 10^{-3}$

$\alpha =\frac{A \text {ctual ionisation}}{\text {Molar concentration}}$

$\%$ of acid dissociated $=10^{-2} \times 1.00$

$=1 \%$