Question

The number \[1 . \bar{{27}}\] in the form \[\frac{p}{q}\] , where p and q are integers and q ≠ 0, is

Options

• \[\frac{14}{9}\]

• \[\frac{14}{11}\]

• \[\frac{14}{13}\]

• \[\frac{14}{15}\]

Answer 1

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`