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Express 0.9999… as a fraction in simple ...

Express 0.9999… as a fraction in simple form.

Text Solution

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Let `x = 0.9999….." "….(i)`
Since the repeating block has only digit 9, we m multiply x by 10 to get
`10x = 9.9999… " "….(ii)`
Subtracting (i) from (ii) , we get
`9x = 9 hArr x = 1`
Hence, 0.9999....=1.
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