jmc

We could simply start dividing and look for a pattern, but there is a cooler way using the fact that $1=.\overline{9999}$. Then $$\begin{array}{rl}\frac{1}{1111}& =\frac{.\overline{9999}}{1111}\\ & =.\overline{0009}.\end{array}$$The first 40 digits after the decimal point consist of ten blocks of $0009$, so their sum is $10\cdot (0+0+0+9)=\boxed{90}$.