Question

Express the following decimal as a rational number.

4.6724

Answer 1

Let x = 4.6724
= 4.6724724...
Here, only numbers 724 is being repeated, so first we need to remove 6 which proceeds 724.
We multiply by 10 so that only the recurring digits remain after decimal.
∴ 10x = 46.724724....        ....(1)
The number of digits recurring in equation (1) is 3, so we multiply both sides of the equation (1) by 1000.
∴ 10000x = 1000 x 46.724724...
= 46724.724....       ....(2)
On subtracting (1) from (2), we get
9990x = 4678

∴ x = `(46678)/(9990)`

= `(23339)/(4995)`

∴ 4.6724 = `(763)/(999)`

= `(23339)/(4995)`