how do you name fractions as a repeating terminating decimal

Question

for middle school

Answer 1

Look at the denominator. If it can be factored into twos and/or fives only, then it will be a terminating decimal. Otherwise it will be a repeating decimal. 

EXAMPLES

7/16 is terminating because only 2 and its powers go into 16.

32/125 is terminating because 125 factors into 5 and its powers.

43/250 is terminating because only 2s and 5s go into 250.

2/15 is repeating because 15 contains a factor which isn’t 2 or 5, namely 3.

59/70 is repeating because 7 is a factor of 70, and 7 isn’t 2 or 5.