Calculate the concentration of hydrogen ions $[H^+]$ in the following solutions: $(a)$ $0.001 \ M \ HNO_3$ $(b)$ $0.0001 \ M \ KOH$.

(A) $HNO_3$ is a strong acid,so $[H^+] = [HNO_3] = 0.001 \ M = 1.0 \times 10^{-3} \ M$.
$(b)$ $KOH$ is a strong base,so $[OH^-] = [KOH] = 0.0001 \ M = 1.0 \times 10^{-4} \ M$.
Using the ionic product of water,$K_w = [H^+][OH^-] = 1.0 \times 10^{-14}$.
$[H^+] = \frac{K_w}{[OH^-]} = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-4}} = 1.0 \times 10^{-10} \ M$.