Question

What is the condition for the decimal expansion of a rational number to terminate? Explain with the help of an example.

Answer 1

Solution: Let x = p/q be a rational number, such that the prime factorization of q is of the form 2^m5ⁿ, where n, m are non-negative integers. Then x has a decimal expansion which terminates. 

Example:

Since the denominator is of the form 2^m x 5ⁿ, the rational number has a terminating decimal expansion.