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Hurkyl
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Mar28-11, 07:19 PM
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Quote Quote by apeiron View Post
:sigh: If only the answer were so simple as long division.

As should be clear, the issue is the precision. The answer for simple constructive operations is always going to be exact. But for division, answers are only going to be effective. You have to introduce a cut-off on the number of decimal places as a further pragmatic choice.
Please try to be far more specific than you have been. I have to guess at the fine details of what you mean.


Long division is an exact operation on decimal numerals. Every computable operation on real numbers will have to deal with precision issues of some sort. Even addition.

When applied to decimals that represent rational numbers (because at some point a sequence of digits repeats forever), a slight modification allows long division to terminate after a finite number of steps.


Incidentally, when applied to rational numbers represented as a quotient of integers, the division algorithm and multiplication algorithms are pretty much identical.