Question

Express the following in the form of $\frac{p}{q}$.

0.4747....

• A. $\frac{47}{991}$
• B. $\frac{47}{9}$
• C. $\frac{47}{919}$
• D. $\frac{47}{99}$

Answer 1

The correct option is D $\frac{47}{99}$

Let $x=\mathrm{0.4747....}$

The periodicity of the decimal is $2$, therefore, multiply $x$ by $100$ as shown below:

$100\times x=100\times \mathrm{0.4747....}\Rightarrow 100x=\mathrm{47.474747....}$

Now, we find the value of $x$ in the form of fraction as shown below:

$100x-x=\left(\mathrm{47.474747....}\right)-\left(\mathrm{0.4747....}\right)\Rightarrow 99x=47\Rightarrow x=\frac{47}{99}$

Hence, $\mathrm{0.4747....}=\frac{47}{99}$.