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  1.  
  2.  
    today's repeating decimal:

    0.0001188118811881188118811881188118811881188118811.....
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      CommentAuthorAngus
    • CommentTimeJul 7th 2020
     
    What's the easy algorithm for turning that back into a rational fraction?
  3.  
    I think Al wants us to guess.

    In which case, I smell a 9 in there somewhere
    •  
      CommentAuthorAngus
    • CommentTimeJul 7th 2020
     
    Or a 11.
  4.  
    Actually, we figured out (something of) what it took to create these repeating fractions a while back, and called them "moletrap numbers" until we found their real name.
  5.  
    What's the current that a 12 volt source will push through 101,000 ohms of resistance?
    •  
      CommentAuthorAngus
    • CommentTimeJul 7th 2020
     
    Yes exactly.
    Or approximately...
    But I don't think we figured out how to go the other direction.
    • CommentAuthorAsterix
    • CommentTimeJul 7th 2020
     
    Would it be a valid observation that repeating decimals can be represented as a non-repeating "decimal" in another integer base? For example, what's that decimal in base 12?
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      CommentAuthorAngus
    • CommentTimeJul 7th 2020
     
    For the record it is


    0.00025692b263152656bb94962aa00859ba13428b34b29330615bb965290958a69565002725911bb36201a87930870929
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      CommentAuthorgoatcheez
    • CommentTimeJul 7th 2020
     
    That would be 'duodecimal'.
    • CommentAuthorAsterix
    • CommentTimeJul 7th 2020
     
    If that's a repeating "duodecima", the period appears to be very long...
    • CommentAuthorAsterix
    • CommentTimeJul 7th 2020
     
    Posted By: alsetalokinWhat's the current that a 12 volt source will push through 101,000 ohms of resistance?


    The same as pushing 6V through 50,500 ohms or 3V through 25,250 ohms.
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      CommentAuthoralsetalokin
    • CommentTimeJul 7th 2020 edited
     
    Posted By: AsterixIf that's a repeating "duodecima", the period appears to be very long...

    I've seen longer repeats in decimal. I don't give up looking for a repeat until the calculator runs out of available or computable digits.





    Posted By: Asterix
    Posted By: alsetalokinWhat's the current that a 12 volt source will push through 101,000 ohms of resistance?


    The same as pushing 6V through 50,500 ohms or 3V through 25,250 ohms.


    Which non-unique factoring might make it difficult to find a reverse algorithm. On the other hand, are there repeating decimals that cannot be factored in multiple ways? Or cannot be factored at all?
  6.  
    Yup
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      CommentAuthorAngus
    • CommentTimeJul 7th 2020 edited
     
    Al's original fraction is 12/101000. This is equal to 12(1/101)*1/1000.
    1/101=0.0099009900990099009900990099009900990099009900990099

    101 is prime. The inverses of primes greater than 5 are always repeating decimals.
  7.  
    Thanks
    • CommentAuthorAsterix
    • CommentTimeJul 7th 2020 edited
     
    Isn't 2 / 10 (base 7) = 0.2 (base 7)? Not a repeating fractional part. What I was trying to get at.

    What is the result of the original problem in base 101₁₀?
    •  
      CommentAuthorAngus
    • CommentTimeJul 11th 2020 edited
     
    Posted By: AsterixWould it be a valid observation that repeating decimals can be represented as a non-repeating "decimal" in another integer base? For example, what's that decimal in base 12?


    It just dawned on me that the answer to this is NO. The inverse of any prime number is a repeating decimal. But there is no magical relationship between prime numbers and the base in which they are represented. So. the inverse of any prime number must be a repeating pattern in any base, except the trivial case of the number represented in its own base.

    e.g.

    {7,0.163163163163163163163163163163163163163163163163163163163211}
    {11,0.100000000000000000000000000000000000000000000000000000000011}
    {13,0.093425a17685093425a17685093425a17685093425a17685093425a17711}
    {17,0.07132651a397845907132651a397845907132651a397845907132651a411}
    {19,0.064064064064064064064064064064064064064064064064064064064111}
    {23,0.05296243390a581486771a05296243390a581486771a05296243390a5811}
    {29,0.04199534608387a69115764a272304199534608387a69115764a272304211}
    • CommentAuthorAsterix
    • CommentTimeJul 11th 2020
     
    It's the "trivial" case that I'm talking about.

    Consider a repeating decimal x/y (i.e. not irrational) can always be represented precisely in base y, as the reciprocal of y in base y is always the "trivial" case. Multiply by x and you have a non-repeating "decimal".