find the decimal expansion of 13/80 wothout actual division
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we know that for a fraction in the form of p/q to terminate ,the prime factorisation of q should be in the form of 2^m * 5^n .
And in the given fraction 13/80 ; the prime factorisation of 80 is in that form
80 = 8 * 10
= 2^3 * 5*2
= 2^4 *5^1
Thus, we can say that the fraction 13/80 will have an terminating decimal expansion
Also, with the same condition , we can say that if a fraction is terminating ,then its denominator is in the form of 2^m * 5^n
hence it is terminating
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