Question

Without actual division find wether the given fraction is terminating : 73/365

Answer 1

If the denominator can be written in the form of 2^m * 5^n, where m and n are non negative integers, the fraction will have a terminating decimal expansion. Else if it cannot be written in that form, it eill have a non termihnating decimal expansion. Here first prime factorise 365 ie 365 = 5 * 73 we know 365 = 5 * 73 thus the fraction reduces to 1/5, which has a terminating decimal expansion.