Question

Explain how you know whether 1/15 is equal a terminating decimal or

Answer 1

The lame answer is that you put it into a calcuator and see.

The more formal way you know is if, when the fraction is reduced, the denominator's only prime factors are 2s or 5s.  If that's the case, the fraction will terminate.  If you have any prime factor other than 2 or 5, it will repeat.

But knowing that "2 or 5 prime factor" idea would have to be something specifically taught in your class (or a prerequisite class).