A definite amount of solid  $N{H}_{4}HS$  is placed in a flask already containing ammonia gas at a certain temperature  and  0.1 atm pressure $N{H}_{4}HS$ decomposes to give  $N{H}_3$ and $H_{2}S$ and at equilibrium. Total pressure in flask is 1.1 atm if the equilibrium constant $K_P$ for the reaction, $N{H}_{4}HS\rightleftharpoons N{H_3}_{\left(g\right)}+H_2{S}_{\left(g\right)}$ is represented as $z\times {10}^{-1}$. Then find value of z ________.