Question

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

$\frac{1111}{(7^4\times {13}^2)}$

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 $\frac{1111}{7^4\times {13}^2}$

Explanation:

Checking denominator:

1. Here the denominator is $7^4\times {13}^2$
2. Which is not in the form $2^n{5}^m$

Conclusion:

1. Hence, $\frac{1111}{7^4\times {13}^2}$is a non-terminating decimal expansion.
2. So, we can not express the given number as a terminating decimal expansion.