jmc

Numbers with exactly one zero have the form $\overline{a0b}$ or $\overline{ab0}$, where the $a,b\ne 0$. There are $(9\cdot 1\cdot 9)+(9\cdot 9\cdot 1)=81+81=\boxed{162}$ such numbers, hence our answer is $\boxed{162}$.