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Question
Express the following decimal as a rational number.
0.89
Solution
Let x = 0.89
Then, x = 0.898989..... ....(1)
Here, the number of digits recurring is 2, so we multiply both sides of the equation (1) by 100.
∴ 100x = 100 x 0.898989....
= 89.8989..... ....(2)
On subtracting (1) from (2), we get
99x = 89
∴ x = `(89)/(99)`
∴ 0.89 = `(89)/(99)`
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