Question

2.50505050... in $\frac{p}{q}$ form is .

• A. $\frac{250}{99}$
• B. $\frac{2455}{999}$
• C. $\frac{248}{99}$
• D. $\frac{358}{99}$

Answer 1

The correct option is C $\frac{248}{99}$

Let $x=\mathrm{2.505050...}$ ... (i)
Multiply both the sides by ${10}^2$ because two digits (50) are repeated after the decimal.
$\Rightarrow 100x=\mathrm{250.505050...}$ ... (ii)
Subtract equation (i) from equation (ii), we get,
$100x-x=\mathrm{250.505050...}-\mathrm{2.505050...}$
$\Rightarrow$ $99x=248$
$\Rightarrow x=\frac{248}{99}$