Raul wrote:
>
> Since this started out as rounding of money type we also need to look at
> that aspect  :  for example it may make sense to always round up taxes, etc.
>
> There is a pretty cool overview of various rounding algorithms here :
> http://www.diycalculator.com/popup-m-round.shtml
>
> Raul
>
> > Math is based upon principles. The principle of rounding is
> > to minimize errors. That is why 4.3 is about 4, not 5. When
> > the last digit is 5, we have to alernate rounding so that
> > one is not unfairly weighted. Rounding to odd would cause
> > problems at 0, and so rounding to even is the way.

Question: What to do about 5? How do we round 3.45 to
tenths? We have to be
fair, and rounding up is not fair! Round to even:
3.45 ~ 3.4
3.55 ~ 3.6
In one case we rounded down, the other we rounded up. This
is fair!

Why not round to odd? 3.45 ~ 3.5? Answer: Suppose we wanted
to round it
again. We would get 3.45 ~ 3. Rounding to even avoids the 5,
and so avoids the
double rounding error.

I do not care about all the possible rounding algorithms out
there. The only one that makes sense is round to even.
Please let us not agree to things that do not make sense.

Sanford Aranoff wrote:

> Raul wrote:
> >
> > Since this started out as rounding of money type we also need to
> > look at that aspect  :  for example it may make sense to always
> > round up taxes, etc.
> >
> > There is a pretty cool overview of various rounding algorithms here
> > :  http://www.diycalculator.com/popup-m-round.shtml
> >
> > Raul
> >
> > > Math is based upon principles. The principle of rounding is
> > > to minimize errors. That is why 4.3 is about 4, not 5. When
> > > the last digit is 5, we have to alernate rounding so that
> > > one is not unfairly weighted. Rounding to odd would cause
> > > problems at 0, and so rounding to even is the way.
>
> Question: What to do about 5? How do we round 3.45 to
> tenths? We have to be
> fair, and rounding up is not fair! Round to even:
> 3.45 ~ 3.4
> 3.55 ~ 3.6
> In one case we rounded down, the other we rounded up. This
> is fair!
>
> Why not round to odd? 3.45 ~ 3.5? Answer: Suppose we wanted
> to round it
> again. We would get 3.45 ~ 3. Rounding to even avoids the 5,
> and so avoids the
> double rounding error.
>
> I do not care about all the possible rounding algorithms out
> there. The only one that makes sense is round to even.
> Please let us not agree to things that do not make sense.

Sanford

What makes sense to you doesn't necessarily make sense to others and
certainly not in different contexts.

Did you actually read the reference given
(http://www.diycalculator.com/popup-m-round.shtml) and the arguments
for and against each algorithm?  Whether you care or not about all the
possiblities, they exist for a reason.

I'm making a big, big cake and I need 2.5 kg of sugar.  Sugar comes in
1 kg bags, so I must round UP to 3 kg because if I round to EVEN and
buy just 2 bags I won't have enough sugar for my cake.  So in this
context round UP makes sense. And minimises errors!

Munch, Munch

Jeff

--
Jeff Cook
Aspect Systems Ltd
www.aspect.co.nz
+
Joan and Jeff Cook
The Cooks Oasis
www.cookislandsoasis.com

Jeff Cook wrote:

> Sanford Aranoff wrote:
>
> > Raul wrote:
> > >
> > > Since this started out as rounding of money type we also need to
> > > look at that aspect  :  for example it may make sense to always
> > > round up taxes, etc.
> > >
> > > There is a pretty cool overview of various rounding algorithms
> > > here :  http://www.diycalculator.com/popup-m-round.shtml
> > >
> > > Raul
> > >
> > > > Math is based upon principles. The principle of rounding is
> > > > to minimize errors. That is why 4.3 is about 4, not 5. When
> > > > the last digit is 5, we have to alernate rounding so that
> > > > one is not unfairly weighted. Rounding to odd would cause
> > > > problems at 0, and so rounding to even is the way.
> >
> > Question: What to do about 5? How do we round 3.45 to
> > tenths? We have to be
> > fair, and rounding up is not fair! Round to even:
> > 3.45 ~ 3.4
> > 3.55 ~ 3.6
> > In one case we rounded down, the other we rounded up. This
> > is fair!
> >
> > Why not round to odd? 3.45 ~ 3.5? Answer: Suppose we wanted
> > to round it
> > again. We would get 3.45 ~ 3. Rounding to even avoids the 5,
> > and so avoids the
> > double rounding error.
> >
> > I do not care about all the possible rounding algorithms out
> > there. The only one that makes sense is round to even.
> > Please let us not agree to things that do not make sense.
>
> Sanford
>
> What makes sense to you doesn't necessarily make sense to others and
> certainly not in different contexts.
>
> Did you actually read the reference given
...and I have to round in accordance with the international rules for
my sport.  They work on the principle of 'giving the benefit of the
doubt' to the competitor so they always round up.  Just as fair!




--