Question

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

(i) `2. bar (24)`

Answer 1

Let x = ` bar (2.24)`
∴ x = 2.2444                    …(1)
10x = 22.444                    …(2)
100x = 224.444                  …(3)
On subtracting equation (2) from (3), we get
90x = 202 ⇒ x =` 202/90 = 101/45`
∴ `bar (2.24) = 101/45`