The solubility of a salt of weak acid (AB) at $P^{H}3$ is $Y\times {10}^{-3}mol{L}^{-1}.$ The value of Y is ___
(Given that the value of solubility product of AB $\left(Ksp\right)=2\times {10}^{-10}$ and the value of ionization constant of $HB\left(K_a\right)=1\times {10}^{-8}$ ) $(p{k}_w=14)$

 $\begin{array}{l}AB\Rightarrow A^{+}+B^{-}\\ s(s-x)\\ 2\times {10}^{-10}=S(S-x)\mathrm{..........}\left(1\right)\\ B^{-}+H^{+}\Rightarrow HB\\ (S-x){10}^{-3}x\\ \frac{x}{S-x}={10}^5\mathrm{...................}\left(2\right)\end{array}$
 Multiply equation (1) and (2)
  $\begin{array}{l}Sx=2\times {10}^{-5}\\ FromEq.\left(1\right)\\ S^2-Sx=2\times {10}^{-10}\\ S^2-2\times {10}^{-5}=2\times {10}^{-10}\\ S^2=2\times {10}^{-5}+2\times {10}^{-10}\cong 2\times {10}^{-5}\\ S=4.47\times {10}^{-3}\\ y=4.47\end{array}$