1993 UNCO Math Contest II Problems/Problem 2

Problem

Determine the digit in the place after the decimal point in the repeating decimal for:

Solution

Fist we add them together and divide. We get the repeating decimal .134316134316. We can see that it repeats every six decimal places, so we need to find the remainder when 623 is divided by six. When we divide, we see that the remainder in five, so we go in five decimal places and find 1, and we are done.