Question

Rewrite $0.\overline{24}$ as a simplified fraction.

• A. $\frac{24}{98}$
• B. $\frac{24}{101}$
• C. $\frac{24}{90}$
• D. $\frac{24}{99}$

Answer 1

The correct option is D $\frac{24}{99}$

Let, $x=0.\overline{24}$
$\Rightarrow x=\mathrm{0.242424...}\cdots \left(i\right)$

Here, the repeating digits are 24.

Step 1: Place the repeating digits to the left of the decimal point by multiplying it by 100 because the unit digit in the hundredths place
$\Rightarrow 100\times x=100\times \mathrm{0.242424...}$
$\Rightarrow 100x=\mathrm{24.2424...}\cdots \left(ii\right)$

Step 2: Place the repeating digit to the right of the decimal point.

In equation $\left(i\right),$ the repeating digit is already to the right.

Now, from $\left(ii\right)-\left(i\right),$ we get
$100x-x=\mathrm{24.242424...}-\mathrm{0.242424...}$
$\Rightarrow 99x=24$
Dividing both the sides by 99, we get
$\Rightarrow \frac{99x}{99}=\frac{24}{99}\Rightarrow x=\frac{24}{99}$