Question

if a/b is a rational number (b is not equal to 0) in its lowest form. what is the condition on b so that the decimal representation of a/b is terminating.

Answer 1

aloha user!!


we are having one rational number => a/b

where b is not equal to 0.

for this to be terminating the prime factorization of b should be in the form $2^{m} or/and.. 5^{n}$

where m and n are natural numbers.


moreover, the prime factorization should not have any number other than 2 or 5.


for example 55/4 => 55/ 2 × 2 => because 2 is there in the prime factorization so we can say that is is terminating.

hope it helps 

good life !!

peace out !!