Math Round problem with ToEven or Away From Zero

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Hi,

According to msdn defenition for rounding methods :

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ToEven - When a number is halfway between two others, it is rounded toward the nearest even number.
AwayFromZero - When a number is halfway between two others, it is rounded toward the nearest number that is away from zero.
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however when trying to use Math.Round i get these results :

double x1 = Math.Round(2.1125, 3, MidpointRounding.ToEven); // Result 2.112
double x2 = Math.Round(2.1125, 3, MidpointRounding.AwayFromZero); // Result 2.113
double x3 = Math.Round(2.1135, 3, MidpointRounding.ToEven); // Result 2.114
double x4 = Math.Round(2.1135, 3, MidpointRounding.AwayFromZero); // Result 2.114

double y1 = Math.Round(2.125, 2, MidpointRounding.ToEven); // Result 2.12
double y2 = Math.Round(2.125, 2, MidpointRounding.AwayFromZero); // Result 2.13
double y3 = Math.Round(2.135, 2, MidpointRounding.ToEven); // Result 2.13
double y4 = Math.Round(2.135, 2, MidpointRounding.AwayFromZero); // Result 2.13

when rounding 3 decimals the result is expected.
but when rounding 2 decimals I get a wrong result.

y3 should return 2.14 because we are rounding to EVEN numbers.
y4 should return 2.14 becuase we are rounding away from zero.

I dont understand the results. Can anyone please explain them to me ?

Eldad.

Posted 4-May-13 21:15pm

Eldad-p

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Richard MacCutchan 5-May-13 3:18am

Floating point numbers always produce strange results because of the way they are represented in computers; they are approximations of real numbers.

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Ian A Davidson · Answer 1 · 2013-05-04T21:29:00

Solution 1

See the "Notes to Callers" on MSDN's page about this method: Math.Round(Double, Int32, MidpointRounding)[^]: "Because of the loss of precision that can result from representing decimal values as floating-point numbers or performing arithmetic operations on floating-point values, in some cases the Round(Double, Int32, MidpointRounding) method may not appear to round midpoint values as specified by the mode parameter. ..."
Regards,
Ian.

Posted 4-May-13 21:29pm

Ian A Davidson

Comments

nguyenvansutt 23-Jul-14 1:21am

So how I can round 2.135 -- >2.14 ?
thanks

Ian A Davidson 23-Jul-14 2:31am

Do you mean, how can you overcome the rounding problem?
I expect people have written numerous articles on it, because it is a problem all computers have in one form or another due to the way floating point numbers work.