Question

Without actual division, show that each of the following rational numbers is a non-terminating repeating decimal:

(i) $\frac{11}{2^3\times 3}$

Answer 1

Solution:

Classifying the number as non-terminating repeating decimal:

When the denominator has a factor other than the factor of the form $2^m\times 5^n$(where m and n are positive integers), then rational numbers is a non-terminating repeating decimal.

As the denominator has a factor $\text{'}3\text{'}$other than the factor of the form $2^m\times 5^n$.

Therefore, $\frac{11}{2^3\times 3}$ is a non-terminating repeating decimal.

Final answer: $\frac{\mathbf{11}}{{\mathbf{2}}^{\mathbf{3}}\mathbf{\times }\mathbf{3}}$ is a non-terminating repeating decimal.