Question

Express the following decimal as a rational number.

0.89

Answer 1

Let x = 0.89
Then, x = 0.898989.....       ....(1)
Here, the number of digits recurring is 2, so we multiply both sides of the equation (1) by 100.
∴ 100x = 100 x 0.898989....
= 89.8989.....       ....(2)
On subtracting (1) from (2), we get
99x = 89

∴ x = `(89)/(99)`

∴ 0.89 = `(89)/(99)`