Question

Express the following decimal as a rational number.

0.017

Answer 1

Let x = 0.017
= 0.01717..
Here, only numbers 17 is being repeated, so first we need to remove 0 which proceeds 17.
We multiply by 10 so that the recurring digits remain after decimal.
∴ 10x = 0.1717....        ....(1)
The number of digits recurring equation (1) is 2, so we multiply both sides of the equation (1) by 100.
∴ 1000x = 100 x 0.1717....
= 17.1717....      ....(2)
On subtracting (1) from (2), we get
990x = 17

∴ x = `(17)/(990)`

∴ 0.017 = (17)/(990)