Express each of the following as a rational number in simplest form.
(a) ` 0.overline(6)` (ii) ` 1.overline(8)` (iii) ` 0.1overline6`

Explanation

Let ` x= 0.overline6`. Then ,
x = 0.666…..
10x = 6.666
On subtracting (i) from (ii), we get
9x= 6 ` Rightarrow x = 6/9 = 2/3`
Hence ` 0.overline(6) = 2/3`
(b) Let ` x= 1.overline(8)` then,
x= 1.888
10x= 18.888
On subtracting (i) from (ii),we get
` 9x = 17 Rightarrow x = 17/9 = 1""8/9`
Hence, ` 1.overline(8) = 1""8/9`
(c) Let `x= 0.1overline(6)` , then
x = 0.1666
10x= 1.6666
And , 100x = 16.6666
On subtracting (ii) from (iii),we get
90x = 15 ` Rightarrow x 15/90 = 1/6`
` 0.1overline6= 1/6`