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Question
Express the following decimal as a rational number.
0.017
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Solution
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)
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