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Let x = .132132132132... By considering..?

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Let x = .132132132.. by considering 100x-x, express x in the form m/n, where m and n are integers.

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  1. x =0 .132132132132, so

    100x = 132.132132132

    Clearly 99x = 132 so x = 132/99


  2. x = 0.132132...

    1000x = 132.132132...

    1000x - x = 132.132132... - 0.132132...

    999x = 132

    x = 132/999

    x = 44/333

    ∴ 0.132132... = 44/333
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