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Question
Express the following decimal as a rational number.
17.027
Solution
Let x = 17.027
= 17.027777..
Here, only number 7 is being repeated, so first we need to remove 02 which proceeds 7.
We multiply by 100 so that only the recurring digits remain after decimal.
∴ 100x = 1702.7777.... ....(1)
The number of digits recurring in equation (1) is 1, so we multiply both sides of the equation (1) by 10.
∴ 1000x = 10 x 1702.7777....
= 17027.7774..... ....(2)
On subtracting (1) from (2), we get
900x = 15325
∴ x = `(15325)/(900)`
= `(613)/(26)`
∴ 17.027 = `(613)/(36)`
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