Question

Express the following decimal as a rational number.

0.35

Answer 1

Let x = 0.35
Then, x = 0.353535.....      ....(1)
Here, the number of digits recurring is 2, so we multiply both sides of the equation (1) by 100.
∴ 100x = 100 x 0.353535.... 
= 35.3535.....                    ....(2)
On subtracting (1) from (2), we get
95x = 35

∴ x = `(35)/(99)`

∴ 0.35 = `(35)/(99)`