Question

If $\mathrm{2.5252525...}$ $=\frac{p}{q}$(in the lowest form), then what is the value of $\frac{q}{p}$?

• A. $0.4$
• B. $0.42525$
• C. $0.0396$
• D. $0.396$

Answer 1

The correct option is D $0.396$

Let $x=\mathrm{2.525252....}$

Then $100\times x=\mathrm{252.525252....}$

Thus, $100x-x=\mathrm{252.525252....}-\mathrm{2.52525252...}=250$

$99x=250$

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

$\therefore \frac{p}{q}=\frac{250}{99}$

Taking reciprocals, $\frac{q}{p}=\frac{99}{250}=0.396$