Question

\[23 .  \bar{{43}}\] when expressed in the form \[\frac{p}{q}\] (p, q are integers q ≠ 0), is

Options

• \[\frac{2320}{99}\]

• \[\frac{2343}{100}\]

• \[\frac{2343}{999}\]

• \[\frac{2320}{199}\]

Answer 1

Given that `23.overline43`

Now we have to express this number into the form of `p/q`
Let

\[x = 23 . 43\]

\[x = 23 + 0 . 4343 . . . \]

\[x = 23 + \frac{43}{99}\]

\[x = \frac{2277 + 43}{99} = \frac{2320}{99}\]

`⇒ 23.overline43 = 2320/99`