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Math.Round Method (Double, Int32, MidpointRounding)

Updated: March 2012

Rounds a double-precision floating-point value to the specified number of fractional digits. A parameter specifies how to round the value if it is midway between two other numbers.

Namespace:  System
Assembly:  mscorlib (in mscorlib.dll)

'Declaration
Public Shared Function Round ( _
	value As Double, _
	digits As Integer, _
	mode As MidpointRounding _
) As Double
'Usage
Dim value As Double 
Dim digits As Integer 
Dim mode As MidpointRounding 
Dim returnValue As Double 

returnValue = Math.Round(value, digits, _
	mode)

Parameters

value
Type: System.Double

A double-precision floating-point number to be rounded.

digits
Type: System.Int32

The number of fractional digits in the return value.

mode
Type: System.MidpointRounding

Specification for how to round value if it is midway between two other numbers.

Return Value

Type: System.Double
The number nearest to value that has a number of fractional digits equal to digits. If value has fewer fractional digits than digits, value is returned unchanged.

ExceptionCondition
ArgumentOutOfRangeException

digits is less than 0 or greater than 15.

ArgumentException

mode is not a valid value of System.MidpointRounding.

The digits parameter specifies the number of fractional digits in the return value and ranges from 0 to 15. If digits is zero, then an integer is returned.

The mode parameter controls how value is rounded if there is a single digit in value to the right of the digits decimal position and its value is 5 — that is, if it is halfway between the digit in the digits position and the next highest digit. The mode parameter can have one of the following two values:

  • MidpointRounding.ToEven. If the digit in the digits position is odd, it is changed to an even digit. Otherwise, it is left unchanged. This behavior follows IEEE Standard 754, section 4. It is sometimes called rounding to nearest or banker's rounding. It minimizes rounding errors that result from consistently rounding a midpoint value in a single direction.

  • MidpointRounding.AwayFromZero. The digit in the digits position is always rounded up to the next digit. This is the most commonly known rounding method. It is known as symmetric arithmetic rounding.

The maximum total number of integral and fractional digits that can be returned is 15. If the rounded value contains more than 15 digits, the 15 most significant digits are returned. If the rounded value contains 15 or fewer digits, the integral digits and as many fractional digits as the digits parameter specifies are returned.

Notes to Callers:

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. This is illustrated in the following example, where 2.135 is rounded to 2.13 instead of 2.14. This occurs because internally the method multiplies value by 10digits, and the multiplication operation in this case suffers from a loss of precision.

Module Example
   Public Sub Main()
      Dim values() As Double = { 2.125, 2.135, 2.145, 3.125, 3.135, 3.145 }
      For Each value As Double In values
         Console.WriteLine("{0} --> {1}", value, _ 
                           Math.Round(value, 2, MidpointRounding.AwayFromZero))
      Next 
   End Sub 
End Module 
' The example displays the following output: 
'       2.125 --> 2.13 
'       2.135 --> 2.13 
'       2.145 --> 2.15 
'       3.125 --> 3.13 
'       3.135 --> 3.14 
'       3.145 --> 3.15

The following code example demonstrates how to use the Round method with the MidpointRounding enumeration. Although the code example rounds decimal numbers, the Round method rounds double-precision floating-point numbers in a similar way.

' This example demonstrates the Math.Round() method in conjunction  
' with the MidpointRounding enumeration. 
Imports System

Class Sample
    Public Shared Sub Main() 
        Dim result As Decimal = 0D
        Dim posValue As Decimal = 3.45D
        Dim negValue As Decimal = -3.45D

        ' By default, round a positive and a negative value to the nearest even number.  
        ' The precision of the result is 1 decimal place.
        result = Math.Round(posValue, 1)
        Console.WriteLine("{0,4} = Math.Round({1,5}, 1)", result, posValue)
        result = Math.Round(negValue, 1)
        Console.WriteLine("{0,4} = Math.Round({1,5}, 1)", result, negValue)
        Console.WriteLine()

        ' Round a positive value to the nearest even number, then to the nearest number  
        ' away from zero. The precision of the result is 1 decimal place.
        result = Math.Round(posValue, 1, MidpointRounding.ToEven)
        Console.WriteLine("{0,4} = Math.Round({1,5}, 1, MidpointRounding.ToEven)", _
                           result, posValue)
        result = Math.Round(posValue, 1, MidpointRounding.AwayFromZero)
        Console.WriteLine("{0,4} = Math.Round({1,5}, 1, MidpointRounding.AwayFromZero)", _
                           result, posValue)
        Console.WriteLine()

        ' Round a negative value to the nearest even number, then to the nearest number  
        ' away from zero. The precision of the result is 1 decimal place.
        result = Math.Round(negValue, 1, MidpointRounding.ToEven)
        Console.WriteLine("{0,4} = Math.Round({1,5}, 1, MidpointRounding.ToEven)", _
                            result, negValue)
        result = Math.Round(negValue, 1, MidpointRounding.AwayFromZero)
        Console.WriteLine("{0,4} = Math.Round({1,5}, 1, MidpointRounding.AwayFromZero)", _
                           result, negValue)
        Console.WriteLine()

    End Sub 'Main
End Class 'Sample

'This code example produces the following results: 

' 3.4 = Math.Round( 3.45, 1) 
'-3.4 = Math.Round(-3.45, 1) 

' 3.4 = Math.Round( 3.45, 1, MidpointRounding.ToEven) 
' 3.5 = Math.Round( 3.45, 1, MidpointRounding.AwayFromZero) 

'-3.4 = Math.Round(-3.45, 1, MidpointRounding.ToEven) 
'-3.5 = Math.Round(-3.45, 1, MidpointRounding.AwayFromZero) 
'

Windows 7, Windows Vista, Windows XP SP2, Windows XP Media Center Edition, Windows XP Professional x64 Edition, Windows XP Starter Edition, Windows Server 2008 R2, Windows Server 2008, Windows Server 2003, Windows Server 2000 SP4, Windows Millennium Edition, Windows 98

The .NET Framework and .NET Compact Framework do not support all versions of every platform. For a list of the supported versions, see .NET Framework System Requirements.

.NET Framework

Supported in: 3.5, 3.0, 2.0

Date

History

Reason

March 2012

Clarified the operation of midpoint rounding.

Customer feedback.

May 2010

Added the Notes for Callers section.

Customer feedback.

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