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

Explanation

(i) Let `x=4.3bar2`
Since there is one digit after decimal and not under the bar, multiply by 10 on both sides.
`10x=4.3bar2xx10`
`10x=43.bar2`
`10x=43+0.bar2`
`10x=43+2/9`
​`10x=(43xx9+2)/9=389/9`
​`x=389/90`
(ii) Let `x=15.7bar12`
Since there is one digit after decimal and not under the bar, multiply by 10 on both sides.
`10x=15.7bar12xx10`
`10x=157.bar12`
`10x=157+0.bar12`
`10x=157+4/33`
​`10x=(157xx33+4)/33=5185/33`
​`x=5185/330`