Question

The number $2.525252$ can be written as a fraction, when reduced to the lowest term, the sum of the numerator and denominator is:

• A. $7$
• B. $29$
• C. $141$
• D. $349$

Answer 1

The correct option is D $349$

Let the given number be $x=\mathrm{2.525252....}$

multiplying with $100$ on both sides

$\Rightarrow 100x=\mathrm{252.525252...}$

$\Rightarrow 100x=250+\mathrm{2.5252...}$

$\Rightarrow 100x=250+x\Rightarrow 99x=250$

$\Rightarrow x=\frac{250}{99}$

$\therefore$ Sum of numerator and denominator $=25099=349$