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2005 ]
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Lynn H. Maxson wrote:
> Peter,
>
> "You gotta be kidding. They teach fractional arithmetic in
> junior high. And those kids still do it by hand. And they get
> the right answer (if they pass the course)."
>
> Fractional arithmetic that produces a real number? To how
> many places? If you come up with a result that is expressed
> as a fraction with a numerator and denominator, you don't
> have a real number. Period. You can take 2/3 of 6 (4), but
> you can't take 2/3 of 7 (4.??????...). You can't do it in
> fractional arithmetic except as 14/3.
What I don't understand in y'all's argument is why the answer to 2/3 * 7 can't simply be 14/3. That
is what I teach my students. I grumble and complain if they use 4.66...7 or 4 2/3. I want
fractions! including improper ones. I keep telling my students "fractions are your friend." They
don't like it and definitely don't want to believe it. But I insist.
Now I agree at some point, most likely where the answer needs to be transported out of the computer,
an approximate result will have to be tabulated. This can be done at that point to what ever
precision the stack of paper/ink supply will allow. Until then let the numerators and denominators
roll.
Of course, in any machine that has a finite number of bits available the length of either/or both
the numerator and denominator must at some point be truncated. However, with today's multi-gigabit
machines, if your process falls apart because the result is one bit short you are probably over you
head anyhow.
Sheridan
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February |
2005 ]
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