Lets say we prepare a solution of $\ce{HCl}$ with a concentration of $\mathrm{10^{-8}}$. Even on full dissociation (which it will, because it is a strong acid), the $\ce{H+}$ ion concentration due to $\ce{HCl}$ is $\mathrm{10^{-8}}$.
So shouldn't the pH be 8? Is there any factor I am missing? Does the properties of acids change at low concentrations? If so, then how?