Question

What is the condition for decimals expansion of a rational numbers to terminate. Explain with example.

Answer 1

Let $x=p/q$ be a rational number such that the prime factorization of q is of the form $2^m{5}^n$, where n, m are positive integers.

Then x has a decimal expansion which terminates.

Example:

$\frac{49}{500}\times \frac{49}{2^2\times 5^3}$

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