First, the numbers being divided have to be integers (if they are decimals, then these rules might not work).
Fractions that result in terminating decimals involve numbers being divided by: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100... (the numbers go on). The more simple answer would be that the divisor MUST BE either 1, 2, 5 OR some multiple of only these three terms OR the fraction can be reduced such that the divisor follows one of the first two rules. (If the divisor is a multiple of any number other than these, such as 3, 7, 11, then the decimal is not terminating.)
Fractions that result in a reacuring decimal (such as .3333... or .8888...) occur only when the divisor is 3 or 9, or the fraction can be reduced in such a way that the divsor will become 3 or 9. No other divisor (that I can think of) will result in a reacuring decimal.
By a process of elimination, any fraction that does not follow either of the first two rules contains a decimal that is repeating. Examples would be a number divided by 12, 23, 98, etc.