Express each of the following mixed recurring decimals in the form `p/qdot` `4. 3bar2` (ii) `15. 7bar12 `

Explanation

(i) `4. 3bar2`
Let `x=4.32`
Since there is one digit after decimal and not under the bar, multiply by 10 on both sides.
`10x=4.32xx10`
`10x=43.bar2`
`10x=43+0.bar2`
`10x=43+2/9`
`10x=(43×9+2)/9`
`10x=387/9`
`x=387/90`
`therefore` The form of `p/q=387/90`

(ii) `15.7bar12`
Let `x=15.712`
Since there is one digit after decimal and not under the bar, multiply by `10` on both sides.
`10x=15.712xx10`
`10x=157.bar12`
`10x=157+0.bar12`
`10x=157+12/99`
`10x=(157×99+12)/99`
`10x=15555/99`
`x=15555/990=3111/198=1037/66`
`therefore` The form of `p/q=1037/66`