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