
Regarding Calculator and low precision values
What they teach kids in school is a lie. Rounding 5 up produces a bias, because 5 is exactly in the middle. What you should do is round 5 up half the time, and down the other half. IEEE 754 floating point defines a round to even to do this exactly, so Calculator is correct.
Regarding Calculator and low precision values
But doesn't that produce a bias towards even numbers?
Regarding Calculator and low precision values
Whether a number is odd or even is usually not as important as the magnitude of the error. For example, 5.5+3.5+2.5=11. If we round 5 up, we get 6+4+3=13. If we round to even, we get 6+4+2=12. The effect only appears on longer chains of numbers, where the bias of 5 adds up.
Regarding Calculator and low precision values
Under what conditions would you conceivably care about a bias towards even numbers? The main issue is usually whether some measure, the mean for example, becomes biased by rounding. That's what roundtoeven is for.
Regarding Calculator and low precision values
The bias to even numbers would change the shape of the distribution.
The distribution only matters if
you're doing statistics. If you're doing any other branch of math you want to minimize the total error  the distribution is irrelevant.
Rounding towards even minimizes the total error and is the mechanism used internally by most math chips, IIRC. Here's a link that refers to both methods as "equally valid". 
Regarding Calculator and low precision values
Sorry to correct you, but you are wrong.
Regarding Calculator and low precision values
No, thats wrong. If 2 figures are significant, those two figures are exact.
Regarding Calculator and low precision values
I'm sorry, but the site you linked is incomplete. 
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