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Question
Express the following in the form `bb(p/q)`, where p and q are integers and q ≠ 0.
`0.4bar7`
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Solution
Let `x = 0.4bar7`
x = 0.477777 ...(1)
On multiplying equation (1) by 10
⇒ 10x = 4.777 ...(2)
On multiplying equation (2) by 10
⇒ 100x = 47.777
⇒ 100x = 43 + 4.7777
⇒ 100x = 43 + 10x ...[From equation (2)]
⇒ 100x - 10x = 43
⇒ 90x = 43
⇒ `x = 43/90`
∴ `0.4bar7 = 43/90`
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