Question

Convert given Non-terminating repeating decimal into fraction
$0.069696969........$

• A. $\frac{69}{99}$
• B. $\frac{23}{330}$
• C. $\frac{23}{990}$
• D. None of the above

Answer 1

The correct option is B $\frac{23}{330}$

Let 0.0696969...... = K ...........(1)
Multiplying both side by 100 we get,
$\Rightarrow \mathrm{6.96969........}=100K$ .........(2)
Substracting equation (1) from equation (2) we get
$\Rightarrow \mathrm{6.96969....}-\mathrm{0.06969....}=100K-K$
$\Rightarrow 6.9=99K$
$\Rightarrow K=\frac{6.9}{99}$
Removing decimal we get,
$\Rightarrow K=\frac{69}{990}$
On simplifying we get,
$\Rightarrow K=\frac{23}{330}$.