How do you find any digit of a decimal -- look here?!?

Question

For example.
If the fraction is 6/7 and when converted to a decimal it's
0.857142.. and so on.
How do I find for example the 900th digit of this decimal?

Answer 1

This is a repeating decimal. The first, seventh, thirteenth, and so on digits are 8, for example.

Since there are six digits repeating, it's a simple matter to find out what the 900th digit will be; just divide 900 by 6, and note the remainder.

The remainder is 0, so the 900th digit is the same as the "0th" digit, which is also the same as the 6th digit: 2.

Answer 2

This decimal repeats every 6 digits, so divide 900 by 6 and look at the remainder. In this case, the remainder is 0 (or 6), so the 900th digit will be the same as the 6th digit, which is 2.

In general, find the number of digits before the decimal repeats, divide the desired digit position by that number, and use the remainder to count to the desired digit.