
Arithmetic vs. Reality: The Sawdust Principle - douche
http://www.thegrumpyprogrammer.com/2017/03/arithmetic-vs-reality-sawdust-principle.html
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teddyh
Somewhat similarly, it annoys me every time someone rounds off decimals in the
middle of some calculation. You round at the _end_ , not in the middle, _even
if the amount rounded off is tinier than a single atom_. Edward Norton Lorenz
found this out, and called it the “butterfly effect”.

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vanderZwan
I remember being taught about approximations, rounding and significant numbers
near the end of primary school. It was part of explaining why the calculators
we used[0] displayed 1/3 as 0.333333 (because they rounded internally, of
course). And, we were told, because a lot of calculations with calculators had
this rounding error, those last few numbers we saw on the screen would be
incorrect, especially if we did repeated multiplications and additions with
them. So, our maths book instructed, we had to round down our answers to the
same number of digits that we started the calculations with.

This, of course, was not at all the right way to explain what significant
numbers are, but that's how they were introduced to us.

Anyway, I figured that (obviously) rounding after every step would only create
a bigger error, so it would be best to only round at the end to get the best
approximation. Then my teacher docked points for that. One of many _" and I
still kinda feel upset at my teacher for that"_ memories.

