Question

Without doing any actual division, find which of the following rational numbers have terminating decimal representation : ${\displaystyle \frac{123}{250}}$

Answer 1

Given number is ${\displaystyle \frac{123}{250}}$

Since 250 = 2 x 5 x 5 x 5 = 2¹ x 5³
i.e. 250 can be expressed as 2^m x 5ⁿ

∴ ${\displaystyle \frac{123}{250}}$ is convertible into the terminating decimal.