> I hate to spoil all the fun but most TI, Casio, and HP calculators
> already have a "convert-to-fraction" key. I know for certain that the TI-82,
> TI-83, TI-85, TI-86 and TI-92 are models with that capability. The
> limitations on conversion usually fall around 1000+ for the denominator.
The fun for me is in discovering an algorithm which will do this with a given
N-digit decimal. After all, that's what we're all paying $$ for, so it must be
a valuable skill. Let's see. If there's an obvious repetend like, say
2345.2345... repeating, then the infinite geometric series formula applies: (in
this case) 2345*sum(10^(-4n),n,1,inf) = 2345*(1/(1-10^-4) is an integer ratio.
At this the Euclidean algorithm can be used to find the gcf and reduce to lowest
terms.
Considering that the first digits in the decimal are not necessarily part of the
repetend, I wonder what guessing games are played finding ratios when the
repetend is more than half N and or doesn't appear until after the first [N/2]
digits? Any deep throat from Tandy on the list?
G Hagopian
COD
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