Question

Which of the following has non-terminating non-repeating decimal expansion?

• A. $\sqrt{7}$
• B. $25÷5\times 3+7-9÷3$
• C. $\frac{15}{7}$
• D. $\mathrm{2.1340067...}$

Answer 1

Answer: (A), (D)

$\mathrm{2.1340067...}$

We need to find the type of decimal expansion of $\sqrt{7}$
We know that square root of a non-perfect square is always an irrational number.
Hence, type of decimal expansion of $\sqrt{7}$ is non-terminating non-repeating.

$25÷5\times 3+7-9÷3=19.0$
$\Rightarrow 19.0$ is a natural number hence, it's decimal expansion type is terminating decimal.

$\Rightarrow \frac{15}{7}=$$2.\overline{142857}$Here, type of decimal expansion is a non-terminating repeating.

$\mathrm{2.1340067..}$ here, type of decimal expansion is non-terminating non-repeating.