Question

The value of $0.2\overline{34}$ is:

• A. $\frac{232}{990}$
• B. $\frac{232}{9990}$
• C. $\frac{232}{909}$
• D. $\frac{232}{9909}$

Answer 1

Answer: (A)

Let,

$x=0.2\overline{34}$

or, $10x=2.\overline{34}=2+0.\overline{34}$

or, $10x-2=.3434.......=0.\overline{34}$.........(1)

or, $100(10x-2)=\mathrm{34.34......}$

or, $100(10x-2)=34+0.\overline{34}$

or, $100(10x-2)=34+10x-2$ [ From (1)]

or, $1000x-200=10x+32$

or, $990x=232$

or, $x=\frac{232}{990}$