Question

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

$\frac{328}{2^2\times 5^3\times 7^4}$

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 $\frac{328}{2^2\times 5^3\times 7^4}$

Explanation:

Checking denominator:

1. Here, the denominator is $2^2\times 5^3\times 7^4$.
2. Which cannot be written in the form $2^n{5}^m$.

Conclusion:

1. Hence, the given number is a non-terminating decimal number.
2. So, we cannot express the given number in terminating decimal expansion.