Weak monobasic acid ionises in water to give $H _{3} O ^{+}$ion according to equation,
$HA + H _{2} O \leftrightharpoons H _{3} O ^{+} A$
Let $\alpha$ be the degree of ionisation then the concentration of various species at equilibrium.
$HA + H _{2} O \leftrightharpoons H _{3} O ^{+}+ A$
$\begin{array}{cccc}\text { Initialconcentration } & 0.1 & 0 & 0 \\ \text { Conc.atequilibrium } & 0.1(1-\alpha) & 0.1 \alpha & 0.1 \alpha\end{array}$
$[\therefore \alpha$ is very small and negligible as compared to $1 .]$
Now, $K _{ a }=\frac{0.1 \alpha \times 0.1 \alpha}{1}$
or $K _{ a }=0.1 \alpha^{2}$
But $K _{ a }=1 \times 10^{-5}$, (given)
$\therefore 1 \times 10^{-5}=0.1 \alpha^{2}$
or $\alpha=\sqrt{\frac{10^{-5}}{0.1}}$
$=10^{-2}=0.01$
Hence, degree of ionisation $=0.01$ and percentage of ionisation
$=0.01 \times 100=1 \%$