Express each of following decimals in the form `p/q` (i) `0. bar4` (ii)`0. bar5` (iii)`0. bar6`

Explanation

(i) Let `x=0.bar4=0.4444....` ....(i)
multiple with 10 both side :
`10x=4.4444....` ....(ii)
Subtracting (i) from (ii)
`9x=4`
⇒`x=4/9`
∴`0.bar4=4/9`
(ii) Let `x=0.bar5=0.55555....` ....(i)
multiple with 10 both side :
`10x=5.5555....` ....(ii)
Subtracting (i) from (ii)
`9x=5`
⇒`x=5/9`
∴`0.bar5=5/9`
(iii) Let `x=0.bar6=0.6666....` ....(i)
multiple with 10 both side :
`10x=6.6666....` ....(ii)
Subtracting (i) from (ii)
`9x=6`
⇒`x=6/9`
∴`0.bar6=6/9`
`=>` `0.bar6=2/3`