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21-11-2017
Mathematics

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Express 9.21212121212... as a rational number, in the form pq

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LammettHash LammettHash

21-11-2017

[tex]x=9.212121\ldots=9.\overline{21}[/tex]
[tex]100x=921.212121\ldots=921.\overline{21}[/tex]
[tex]99x=921.\overline{21}-9.\overline{21}=921-9=912[/tex]
[tex]\implies x=\dfrac{912}{99}=\dfrac{304}{33}[/tex]

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