Question

Which of the following fraction is recurring decimal?

• A. $\frac{2}{5}$
• B. $\frac{13}{8}$
• C. $\frac{5}{2}$
• D. $\frac{3}{7}$

Answer 1

The correct option is D $\frac{3}{7}$

If the denominator of a fraction cannot be written with a power of 10, then the decimal form of the fraction continues indefinitely. This type of decimal is called recurring decimal.

Here, the denomiators of $\frac{2}{5}$, $\frac{13}{8}$, $\frac{5}{2}$ can be written with a power of 10.

$\Rightarrow$ $\frac{2}{5}\times \frac{2}{2}=\frac{4}{10}$

$\Rightarrow$ $\frac{13}{8}\times \frac{125}{125}=\frac{1625}{1000}$

$\Rightarrow$ $\frac{5}{2}\times \frac{5}{5}=\frac{25}{10}$

But the denominator of the fraction $\frac{3}{7}$ cannot be written as power of 10. So, the decimal form of $\frac{3}{7}$ will be a recurring decimal.