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From: Joel Koltner on 9 Apr 2010 19:36
"Han" <handuongster(a)gmail.com> wrote in message
news:74be1d5d-ca67-454c-b791-426829a6b737(a)u34g2000yqu.googlegroups.com...
On Apr 9, 5:28 am, "Tom Lake" <tl...(a)twcny.rr.com> wrote:
>I think the point was that there are students who "don't think" about
>such details and are clueless as to why when they obtain unexpected
>answers.

Even for students who think a little, this problem can come up unexpectedly:
While it's pretty clear in the example given what the limitation is, the
regular old textbook quadratic formula has the same problem for one root in
that you have... -b + sqrt(b^2-4ac) -- so when 4ac is small (relative to b^2),
the expression often becomes zero or at least something highly inaccurate.

Most formulas can be manipulated to avoid this "small differences of large
numbers" problem, though.

From: Veli-Pekka.Nousiainen on 10 Apr 2010 17:01
Joel Koltner wrote:
> "Han" <handuongster(a)gmail.com> wrote in message
> news:74be1d5d-ca67-454c-b791-426829a6b737(a)u34g2000yqu.googlegroups.com...
> On Apr 9, 5:28 am, "Tom Lake" <tl...(a)twcny.rr.com> wrote:
>> I think the point was that there are students who "don't think" about
>> such details and are clueless as to why when they obtain unexpected
>> answers.
>
> Even for students who think a little, this problem can come up
> unexpectedly: While it's pretty clear in the example given what the
> limitation is, the regular old textbook quadratic formula has the same
> problem for one root in that you have... -b + sqrt(b^2-4ac) -- so when
> 4ac is small (relative to b^2), the expression often becomes zero or at
> least something highly inaccurate.
>
> Most formulas can be manipulated to avoid this "small differences of
> large numbers" problem, though.
>
I used to think but no more
thanks to LongFloat library...
:-)
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