How can you predict whether a fraction will convert to a terminating decimal or a repeating decimal?

Answer 1

If the denominator's only prime factors (if it has any) are 2 and 5, the decimal will terminate; otherwise it won't.

Answer 2

All numbers are in base 10, which has factors 2*5. If the denominator can be broken into a series of 2's and 5's it will be a terminating decimal. For instance, the fraction 3/400 converts into a terminating decimal because 400 can be broken down as 2^4*5^2. The fraction 4/300 cannot because it breaks down to 2^2*3*5^2.

Answer 3

Look at its denominator. If it's only prime factors
are 2 and 5 it the denominator divides a power
of 10 and the decimal will terminate.
Othewise, it will be a repeating decimal.
BTW, the fraction must be in lowest terms
for this rule to work.
Examples: 1/40. 40 = 2³*5 so 1/40 will convert to
a terminating decimal.
1/41 will convert to a repeating decimal.