# 23.43¯¯¯¯ when expressed in the form

Question:

23. $\overline{43}$ when expressed in the form $\frac{p}{q}(p, q$ are integers $q \neq 0)$, is

(a) $\frac{2320}{99}$

(b) $\frac{2343}{100}$

(c) $\frac{2343}{999}$

(d) $\frac{2320}{199}$

Solution:

Given that $23 . \overline{43}$

Now we have to express this number into the form of $\frac{p}{q}$

Let

$x=23.43$

$x=23+0.4343 \ldots$

$x=23+\frac{43}{99}$

$x=\frac{2277+43}{99}=\frac{2320}{99}$

$\Rightarrow 23 . \overline{43}=\frac{2320}{99}$

The correct option is