Let, x=2.134134134… …(i)

Multiplying this equation by 1000 on both the sides so that repetitive terms cancel out and we get:

1000x=2134.134134134… …(ii)

Equation (ii)-(i),

⇒ 1000x-x=2134.134134134-2.134134134=2132

⇒ 999x=2132

⇒