Question

What is the condition for a decimal expansion of a rational number to terminate, explain with example

Answer 1

Let a= p/q be a rational number such that the

prime factorization of q is of the form 25", where n,

mare positive integers.

Then x has a decimal expansion which terminates.

Example:

49

500 22 x 53

Since the denominator is of the form 2" x 5", the

49

rational number has a terminating decimal

expansion.