Math
posted by Hec01
Please help.I need to find two hundredth digit in the decimal representation of each of the following fractions
5/6
4/11
1/13
Thanks.

Steve
5/6 = 0.83333...
4/11 = .363636...
1/13 = .076923 076923 ...
Look at the length of each repeating group. Divide that into 200 to see how many repetitions there are, and what remainder.
For instance
13/70 = .1857 142857 142857 ...
There are 4 leading digits, so that leaves 196. The periodic part has length 6. 196/6 = 32 remainder 4.
So, the 200th digit is
4 + 32*6 + 4
The 4th digit of the repeating part is 8. So, the 200th digit is 8.
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