At 298 K , the limiting molar conductivity of a weak monobasic acid is $4 \times 10^2 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. At 298 K , for an aqueous solution of the acid the degree of dissociation is $\alpha$ and the molar conductivity is $\mathrm{y} \times 10^2 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. At 298 K , upon 20 times dilution with water, the molar conductivity of the solution becomes $3 y \times 10^2 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. The value of $\alpha$ is $\_\_\_\_$ .