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Question
Find the rational form of the number `0.bar(123)`
Solution
Let x = 0.123123123 ... ⇒ x = `0.bar(123)` ...(1)
Multiplying 1000 on both rides
1000x = 123.123123 … ⇒ 1000x = `123 . bar(123)` ...(2)
(2) – (1) = 1000x – x `123.bar(123) - 0.bar(123)`
⇒ 999x = 123
⇒ x = `123/999`
⇒ x = `41/333` Rational number
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