The value of 1.999... in the form of


The value of $1.999$... in the form of $\mathrm{p} / \mathrm{q}$, where $p$ and $q$ are integers and

(a) $\frac{19}{10}$

(b) $\frac{1999}{1000}$

(c) 2

(d) $\frac{1}{9}$



Let $x=1.999 . . .$

Now, $\quad 10 x=19.999 \ldots$

On subtracting Eq. (i) from Eq. (ii), we get

$10 x-x=(19.999 \ldots)-(1.9999 \ldots)$

$\Rightarrow \quad 9 x=18$

$\therefore$   $x=\frac{18}{9}=2$


Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now