Philosophical Multicore

Sometimes controversial, sometimes fallacious, sometimes thought-provoking, and always fun.

Question of the Week: what is 1/10 in decimals…. in base 3?

Posted by Michael Dickens on May 31, 2007

It might be 0.001111111111111 you get the idea. Not sure.

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7 Responses to “Question of the Week: what is 1/10 in decimals…. in base 3?”

  1. bill said

    It’s 1/101

  2. mtgap said

    It’s 0.002200220022 etc.

    But what is 1/2 in base 5? And what is 1/5 in base 2?

  3. Kelly Dickens said

    By applying the division algorithm, I have calculated:

    1/5 (in base2) = .00110011…

    1/2 (in base 5) = .2222…

  4. Kelly Dickens said

    By following the patterns, I see that, in “base 1”,

    1 would be 1
    2 would be 11
    3 would be 111
    and so on, since the positive powers of 1 are all equal to 1.

    Representing non-integers (such as 1/10) poses a bit of a problem. A big one, really.

  5. Taylor said

    I feel like an idiot

  6. mtgap said

    Taylor, you’ll get it eventually.

  7. mtgap said

    well since 10 is 1111111111, 1/10 would be .000000001 (with 8 zeros or 9?)

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