Question

Write down the decimal expansion of the following rational numbers which have terminating decimal expansion:

$\frac{54}{343}$

Answer 1

Definition of Terminating decimal:

$\frac{p}{q}$ is terminating if

1. p and q are co-prime.
2. q is of the form $2^n{5}^m$
   Where n and m are non-negative integers.

Given Data:

Given number is $\frac{54}{343}$

Explanation:

Checking denominator:

1. Here the denominator is $343=7^3$
2. Which cannot be written as $2^n{5}^m$

Conclusion:

1. Hence, $\frac{54}{343}$is a non-terminating decimal number.
2. So, we cannot express the given number as a terminating decimal number.