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Question
The number \[1 . \bar{{27}}\] in the form \[\frac{p}{q}\] , where p and q are integers and q ≠ 0, is
Options
\[\frac{14}{9}\]
\[\frac{14}{11}\]
\[\frac{14}{13}\]
\[\frac{14}{15}\]
Solution
Given that `1.overline27`
`1.overline27 = 1+27/99`
`⇒ 1.overline27 = (99+27)/99`
`⇒ 1.overline27 = 126/99 `
`⇒ 1.overline27 = (126÷9)/(99 ÷ 9)`
`⇒ 1.overline27 =14/11`
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