Question

Express each of the following as a rational number in its simplest form: 

(i) ` 0. bar(365)`

Answer 1

Let x =`  bar (0.365)`
∴ x = 0.3656565                             …(1)
10x = 3.656565                                  …(2)
1000x = 365.656565                           …(3)
On subtracting equation (2) from (3), we get
990x = 362 ⇒ x = `362/990 = 181/495`
∴ `bar( 0.365 )= 181/495`