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Math Help - 8x

  1. #1
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    8x

    If x=0.1234567891011121314151617181...303132333...





    find  8x
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  2. #2
    Super Member wingless's Avatar
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    x=0.123456789101112131415161718192021...

    This number is called Champernowne Constant.

    It's given by


    Since it's a transcendental number, I can't see a way to multiply it by 8..

    8x = 0.987654312808897051321293745536169778594021018263  4425058667...
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  3. #3
    Senior Member JaneBennet's Avatar
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    Break the number x into chunks, where each chuck starts with a 0 and ends just before the next 0 (and must include some nonzero digits). Multiply each chunk by 8, and then add the chunks up.

    For example, the first chunk is 0.1234567891. Multiply that by 8: 0.9876543128
    The second chunk is 01112131415161718192. Multiply that by 8: 08897051321293745536
    Hence the first 31 digits (30 decimal places) of 8x is: 0.987654312808897051321293745536

    Now continue with the third chunk 022122232425262728293, fourth chunk 03132333435363738394, etc.
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