Question

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

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

Answer 1

The correct option is C

2

Explanation for the correct option:

Option (c): 2

Let, $x=1.999....------------\left(1\right)$

Since, only 1 digit is repeating.

So, multiplying $x$by 10, we get

$10x=19.99....-------------\left(2\right)$

Subtracting equation $\left(1\right)\mathrm{from}\left(2\right)$, we get

$$\begin{gathered} 9x=18 \\ \Rightarrow x=\frac{18}{9} \\ \Rightarrow x=2 \end{gathered}$$

So, the option (c) is correct. The value of $1.999\dots$ in the form$\frac{p}{q}$, where $p$ and $q$ are integers an$q\ne 0$, is 2 .