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Question
Express the following in the form `p/q`, where p and q are integers and q ≠ 0:
`0.bar001`
Solution
Let `x = 0.bar001`
⇒ `x = 0.bar001 = 0.001001` ...(i)
On multiplying both sides of equation (i) by 1000, we get
1000x = 001.001......... ...(ii)
On subtracting equation (i) from equation (ii), we get
1000x – x = 001.001... – (0.001001...)
⇒ 999x = 001
∴ `x = 1/999`
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