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Question
Express each of the following as a rational number in its simplest form:
(i) ` 0. bar(365)`
Solution
Let x =` bar (0.365)`
∴ x = 0.3656565 …(1)
10x = 3.656565 …(2)
1000x = 365.656565 …(3)
On subtracting equation (2) from (3), we get
990x = 362 ⇒ x = `362/990 = 181/495`
∴ `bar( 0.365 )= 181/495`
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