What causes repeating decimals to happen?

Answer 1

If the denominator in the simplest form of a rational number has any prime factor other that 2 or 5 then it will not divide the numerator without remainder. This results in a repeating decimal.

Answer 2

You will get a repeating decimal if the denominator of a fraction has any factor other than 2 or 5.

Suppose there is a factor f. Then f can only leave a remainder of 1, 2, 3, ..., f-1. Whatever order you get these remainders, after at most f-1 digits, you will get a remainder that you had before. This is where the decimal sequence goes into its repeating sequence.