jmc

We can write $0.428125$ in the form $\frac{428,125}{1,000,000}$. Note that $428,000$ and $125$ are divisible by $5^3=125$. Therefore, we can divide numerator and denominator by 125 to obtain $$\begin{array}{rl}\frac{428,125}{1,000,000}& =\frac{125\cdot 3425}{125\cdot 8000}\\ & =\frac{3425}{8000}.\end{array}$$Since 3425 and 8000 are divisible by 25, we can simplify the fraction further: $$\begin{array}{rl}\frac{428,125}{1,000,000}& =\frac{3425}{8000}\\ & =\frac{5^2\cdot 137}{5^2\cdot 320}\\ & =\frac{137}{320}.\end{array}$$The sum of the numerator and denominator is $137+320=\boxed{457}$.