Question

Question 9
The value of 1.999 ….. in the form of $\frac{p}{q}$, where p and q are integers and $q\ne 0$, is

A) $\frac{19}{10}$
B) $\frac{1999}{1000}$
C) $2$
D) $\frac{1}{1}$

Answer 1

The answer is C.
Let x = 1.999 ….(i)
Now, 10x = 19.999………(ii)
On subtracting Eq. (i) from eq (ii) we get,
10x – x = ( 19.999…) – ( 1.999..)
$\Rightarrow$ 9x = 18
$\therefore x=\frac{18}{9}=2$