Find the sum of .

Let’s suppose

We can also divide into two part first one is and second one is

So x = A + B

A = 0.33333……(1)

The repetition start after one digit so we multiplied by 10 in equation (1)

10A = 3.3333……(2)

Subtract the equation (1) from the equation (2)

10A – A = 3.33333….. – 0.3333……

9A = 3

⇒ ……(3)

B = 0.4444….(4)

The repetition start after one digit so we multiplied by 10 in

equation (4)

10B = 4.44444…..(5)

Subtract the equation (4) from the equation (5)

10B – B = 4.444…. - 0.444….

9B = 4

……(6)

x = A + B ⇒