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At 08:54 20/07/2013 -0700, Todor Takov wrote:
I have given my reasons in an explanation to a post by Luuk in this present discussion. But I think this is not an overkill, because if we have a significantly long number and we just look at the 3 digits to the right of the comma separator and just drop the rest of the digits to the right of them - we shall be risking to get an incorrect result. The correct way to round the number will be to start at the rightmost available digit and drop one digit at a time, until we reach the desired digit position. At least this is correct in my opinion.

Paradoxically, this is certainly not the way that rounding - even banker's rounding - is normally achieved.

You would round 1.23456 to 1.2346 and then to 1.235 and 1.24 (using either scheme). Single rounding (again using either scheme) gives 1.23. This makes sense, since the original number is clearly closer to 1.23 than to 1.24.

It is a general principle that you should always round numbers once; if you do so repeatedly, you will indeed get different results. says:
In _Martinez v. Allstate_ and _Sendejo v. Farmers_, litigated between 1995 and 1997, the insurance companies argued that double rounding premiums was permissible and in fact required. The US courts ruled against the insurance companies and ordered them to adopt rules to ensure single rounding.

Some computer languages and the IEEE 754-2008 standard dictate that in straightforward calculations the result should not be rounded twice. This has been a particular problem with Java as it is designed to be run identically on different machines, special programming tricks have had to be used to achieve this with x87 floating point.[...]

Brian Barker

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