1. The problem statement, all variables and given/known data Let E be the set of points in [0,1) whose decimal expansion contains somewhere the block 55555. Find the measure of E. 2. Relevant equations 3. The attempt at a solution I have a feeling that in order to find the measure of E, I should find the measure of the complement of E and then subtract it from 1. The complement of E would be the points in [0,1) containing no 5's, containing no consecutive 5's, containing 2 consecutive 5's, containing 3 consecutive 5's, containing 3 consecutive 5's, or containing 4 consecutive 5's. I'm not sure how to compute the measure of this set, however. Any help would be greatly appreciated!