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Question
Express the following decimal in the form `p/q`: `0.4bar7`
Solution
Let `x=0.4bar7`
`rArr10x=4+0.bar7`
Let `y=0.bar7=0.777....`
⇒ 10y = 7.777...
⇒ 10y = 7 + 0.777...
⇒ 10y = 7 + y
⇒ 10y - y = 7
⇒ 9y = 7
⇒ y = 7/9
`therefore0.bar7=7/9`
Therefore,
`rArr10x=4+7/9`
`rArr10x=(36+7)/9`
`rArr10x=43/9`
`rArrx=43/90`
Hence, `0.4bar7=43/90`
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