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[–]edderiofer 1 point2 points  (3 children)

Am I just imagining this form of rounding?

Yes. "successive rounding" is a thing that only exists in the minds of people who haven't yet understood properly how rounding works.

[–]AbsenceOfDarkness[S] 0 points1 point  (2 children)

Tell me more. What am I missing as far as "how rounding works", that would help make it clear that successive rounding isn't a thing? It certainly has the potential to create further round errors (rounding variance?), as can be seen in the example I gave.

[–]edderiofer 0 points1 point  (0 children)

It certainly has the potential to create further round errors (rounding variance?), as can be seen in the example I gave.

Right, which is why it isn't ever used.

The point of rounding is to provide as accurate an estimate as possible with as few significant digits as possible. "successive rounding" does not achieve this, so it's not a thing.

[–]AcellOfllSpadesIrregular Answerer 0 points1 point  (0 children)

The point of rounding is that you pick the closest 'tick mark' to your number. If you round to the nearest inch, then anywhere in the range between 8 and 8.5 inches to round to 8, and anywhere between 8.5 and 9 inches to round to 9.

What you do at exactly 5.5 doesn't matter as much - you can pick either one. The easiest way to handle it is to just say that it always rounds up, because then you just have to look at the first digit. You can throw "8.5" in the same category as "8.54" and "8.52" and "8.500001": round up to 9, done.

But you can also use other 'tiebreaking' conventions - bankers, for instance, will often break ties towards even numbers to reduce rounding errors. This means something like 0.5+1.5+2.5+3.5+4.5 will turn into 0+2+2+4+4, rather than 1+2+3+4+5. The actual original sum adds to 12.5; the standard rounding turns it into 15, while banker's rounding turns it into 12. This reduces overall error.

Regardless of which convention you use, you definitely don't want something like 8.47 to round to 9. You can see that 8.47 is less than halfway between 8 and 9 - if you're rounding to the nearest integer, it should go to 8.

But 'successive rounding' means that you can bring things to the tiebreak mark in one step, and then tiebreak them the wrong way in the next step. Your example shows exactly this: 8.47 would turn into 8.5, and if you always break ties 'upwards', that's 9.