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प्रश्न
Express the following decimal as a rational number.
4.6724
उत्तर
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)`
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