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Question
\[23 . \bar{{43}}\] when expressed in the form \[\frac{p}{q}\] (p, q are integers q ≠ 0), is
Options
\[\frac{2320}{99}\]
\[\frac{2343}{100}\]
\[\frac{2343}{999}\]
\[\frac{2320}{199}\]
Solution
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`
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