Which digit stands in the 100th place after the decimal point in 5/7?

Long division gives 5/7 = 0.714285 714285 …, a block of 6 digits that repeats for ever. Since $100=6\times 16+4$, the 100th digit is the 4th digit of the block. Counting 7, 1, 4, 2 the answer is 2. Reading the 5th digit instead gives 8 and the 3rd gives 4 — the block position must come from the remainder, not the quotient.