Question

If p/q is a rational no (q ≠0) what condition of q so that the decimal representation of p/q is terminating . ( With solved solution )

Thanks.

Answer 1

For a rational number p/q to have terminating decimal representation, the prime factorisation of q should be of the form 2^m x 5^n, where m and n are non-negative integers.

Example :

Consider the simple example of 50/10.
Here q=10, which can be represented as 2¹ × 5¹ ( m=1 and n =1 ).
Thus it has a terminating decimal expansion, i.e, 0.5

Consider another example of 3/11.
11 cannot be expressed in the prescribed format. Hence it has a reccuring (or repeating) decimal expansion, i.e, 0.2727272727...