Show that each of the following are non-terminating repeating decimal :
(i) `(5)/(12)` (ii) `(7)/(75)`

Explanation

(i) `(5)/(12) = (5)/(2 xx 2 xx 3) = (5)/(2^(2) xx 3)`
`because` the denominator `2^(2) xx 3` is not in the form of `2^(m) xx 5^(n)`
`therefore` it is non-terminating repeating decimal. ` " "`Hence Proved.
(ii) `(7)/(75) = (7)/(3 xx 5 xx 5) = (7)/(3 xx 5^(2))`
`because` the denominator `3 xx 5^(2)` is not in the form `2^(m) xx 5^(m)`
`therefore` it is non-terminating repeating decimal. `" "` Hence Proved.