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Question
Express the following in the form `bb(p/q)`, where p and q are integers and q ≠ 0.
`0.bar001`
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Solution
Let x = `0.bar001` = 0.001001001..... ...(1)
Multiplying both sides by 1000 (since three digits are repeating),
we get 1000x = 1.001001..... ...(2)
(2) - (1)
⇒ 1000x - x = 1
⇒ 999x = 1
⇒ x = `1/999`
Thus, `0.bar001 = 1/999`
Here, P = 1, q = 999 (≠0)
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