How do you know if a decimal is terminating or repeating?

Answer 1

If you know what rational fraction it represents then, if the denominator in the fraction's simplest form has any prime factor other than 2 and 5, then it is a repeating decimal and if not it is terminating.

Otherwise you need to examine the digits of the decimal representation in detail. Remember though, that the repeating string could be thousands of digits long (or even longer).