I was wondering if there was a specific method to follow to decipher terminating from non-terminating, without using a calculator. This is for uncommon numbers like root 6 or 1/7
this is how i think about it for fractions: in the decimal system, the result of dividing one integer by another can be written in terms of the powers of ten. the same applies for fractions. if we have a “clean” power of ten in the denominator, then the fraction will terminate.
trick: we want to have something in the denominator whose prime factorisation is 2(to some power x)*5(to some power y)
example: 1/4 = 1/ 2(power 2)5(power 0) → the denominator is in fact composed of 2 and 5! thus 1/4 must be terminating
1/7 = 1/ 72(power 0)*5(power 0) → the denominator also has a 7. it is not terminating.