Question

Express the following decimal as a rational number.

0.057

Answer 1

Let x = 0.057
Then, x = 0.057057....        ....(1)
Here, the number of digits recurring is 3, so we multiply both sides of the equation (1) by 1000.
∴ 1000x = 1000 x 0.057057....
= 57.057.....        ....(2)
On subtracting (1) from (2), we get
999x = 57

∴ x = `(57)/(999)`

= `(19)/(333)`

∴ 0.057 = `(19)/(333)`