Question

Express the following decimal as a rational number.

0.763

Answer 1

Let x = 0.763
Then, x = 0.763763.....       .....(1)
Here, the number of digits recurring is 3, so we multiply both sides of the equation (1) by 1000.
∴1000x = 1000 x 0.763763....
= 763.763.....        ....(2)
On subtracting (1) from (2), we get
999x = 763

∴ x = `(763)/(999)`

∴ 0.763 = `(763)/(999)`