.NET Math.Round(<double>,<int>,MidpointRounding.AwayFromZero) not working correctly

Question

I am using Visual Studio Professional 2012. I created a new C# ConsoleApplication, targeting .NET Framework 4.5, with following code:

    static void Main(string[] args)
    {
        double x = 2.44445;
        double y = Math.Round(x, 4, MidpointRounding.AwayFromZero);
        Console.WriteLine(y);
        Console.ReadKey();
    }

The expected result should be 2.4445, but it actually returns 2.4444. //Same result with previous framework version, and I tried VCE2010.

I know such problem usually results from the way double data type is stored (i.e. finite decimals converted to infinite binary fraction). But I didn't expect this to happen with only 5 decimal digits like 2.44445

I'm worrying if such thing could happen with even shorter decimals. I would also like to learn a safer way to round (using away from zero convention) in C#. Thanks.

Answer 1

This is indeed due to the fragile precision of floating-point numbers. 0.5 can be stored perfectly in IEEE floating point, but 0.45, 0.445 etc. cannot. For example, the actual value that is stored when you specify 2.44445 is 11009049289107177/4503599627370496 which is 2.44449999999999989519494647... It should now be obvious why the number is rounded the way it is.

If you need to store fractional numbers precisely, consider using the decimal type instead.