Question

Express the following in $\frac{p}{q}$ from $0.\overline{23}$

Answer 1

We have,

$0.2\overline{3}$

Let

$x=0.23$

$\Rightarrow 10x=2.\stackrel{.}{3}$

$\Rightarrow 100x=23.\stackrel{.}{3}$

Now, we know that,

$90x=100x-10x$

$\Rightarrow 90x=23.\stackrel{.}{3}-2.\stackrel{.}{3}$

$\Rightarrow 90x=23-2$

$\Rightarrow 90x=21$

$\Rightarrow x=\frac{21}{90}$

$\Rightarrow x=\frac{7}{30}$

Hence, this is the form of $\frac{p}{q}$

Hence, this is the answer.