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Question
Express the following decimal as a rational number.
0.057
Solution
Let x = 0.057
Then, x = 0.057057.... ....(1)
Here, the number of digits recurring is 3, so we multiply both sides of the equation (1) by 1000.
∴ 1000x = 1000 x 0.057057....
= 57.057..... ....(2)
On subtracting (1) from (2), we get
999x = 57
∴ x = `(57)/(999)`
= `(19)/(333)`
∴ 0.057 = `(19)/(333)`
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