Question

The value of$1.999\dots$ in the form$\frac{\mathrm{p}}{\mathrm{q}}$, where$\mathrm{p}$ and$\mathrm{q}$ are integers and$\mathrm{q}\ne 0$, is

• A. $\frac{19}{10}$
• B. $\frac{1999}{1000}$
• C. $2$
• D. $\frac{1}{9}$

Answer 1

The correct option is C

$2$

Find the value$1.999\dots$ in the form$\frac{\mathrm{p}}{\mathrm{q}}$

Let us assume$\mathrm{x}=1.9999\dots .....\left(1\right)$

Multiply by$10$ on both sides

$10\mathrm{x}=19.9999\dots ..\left(2\right)$

On subtracting the equation$\left(1\right)$ from the equation$\left(2\right)$,

$\begin{array}{rcl}10\mathrm{x}-\mathrm{x}& =& 19.9999....-1.9999...\\ 9\mathrm{x}& =& 18\\ \mathrm{x}& =& \frac{18}{9}\\ \mathrm{x}& =& 2\end{array}$

$\therefore$Hence , The correct option is C.