Express each of the following in the simplest form :
(i) `0.bar(36)` (ii) `1.bar(046)`

Explanation

(i) Let `x = 0.bar(36)`
`rArr` x = 0.363636……. `" "`…(1)
`rArr` 100 x = 36.363636……. `" "` …(2)
Substracting equation (1) from (2), we get
99 x = 36
`rArr` `x = (36)/(99) = (4)/(11)`
`rArr` `0.bar(36) = (4)/(11)`
(ii) Let `x = 1.bar(046)`
`rArr` x = 1.046046046..... `" "` ...(1)
`rArr` 1000x = 1046.046046046.... `" "` ...(2)
Subtracting equation (1) from (2), we get
999x = 1045
`rArr` `x = (1045)/(999) `
`rArr` `1.bar(046) = (1045)/(999)`
(See the shortcut method in "Gold coins")