Question

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

$\frac{1001}{2^0\times 5^3\times {11}^5}$

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 $\frac{1001}{2^0\times 5^3\times {11}^5}$

Explanation:

Checking denominator:

1. Here the denominator is $2^0\times 5^3\times {11}^5$
2. Which cannot be written in the form $2^n{5}^m.$

Conclusion:

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