I know that $\frac{6}{7}$ is a repeating decimal that starts with 0.857142 and then repeats the six digits 857142 indefinitely. So to find the 100th decimal place, I need to figure out which of these six digits is in that position. I can use division to find the remainder when 100 is divided by 6, since that will tell me how many digits are left over after I go through several cycles of the repeating part. 100 divided by 6 is 16 with a remainder of 4, so that means the 100th decimal place is the 4th digit in the repeating part. The 4th digit in 857142 is 1, so that's the answer. 
What numeral is in the 100th decimal place in the decimal representation of $\frac{6}{7}$?