Express each of the following in the simplest form :
(i) `0.bar(6)` (ii) `3.bar(3)`

Explanation

(i) Let `x = 0.bar(6)`
`rArr` x = 0.666……. `" "`…(1)
`rArr` 10 x = 6.666……. `" "` …(2)
Substracting equation (1) from (2) we get
9 x = 6
`rArr` `x = (6)/(9) = (2)/(3)`
`rArr` `0.bar(6) = (2)/(3)`
(ii) Let `x = 3.bar(3)`
`rArr` x = 3.333....... `" "` ...(1)
`rArr` 10x = 33.333...... `" "` ...(2)
Subtracting equation (1) from (2), we get
9x = 30
`rArr` `x = (30)/(9) = (10)/(3)`
`rArr` `3.bar(3) = (10)/(3)`