Why does Math Round 2 5 return 2 instead of 3

Question

In C   the result of Math Round 2 5  is 2   It is supposed to be 3  isn t it  Why is it 2 instead in C

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You should check MSDN for Math Round      The behavior of this method follows IEEE Standard 754  section 4  This kind of rounding is sometimes called rounding to nearest  or banker s rounding    You can specify the behavior of Math Round using an overload   Math Round 2 5  0  MidpointRounding AwayFromZero      gives 3  Math Round 2 5  0  MidpointRounding ToEven      gives 2

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This post has the answer you are looking for   http   weblogs asp net sfurman archive 2003 03 07 3537 aspx  Basically this is what it says   Return Value  The number nearest value with precision equal to digits  If value is halfway between two numbers  one of which is even and the other odd  then the even number is returned  If the precision of value is less than digits  then value is returned unchanged   The behavior of this method follows IEEE Standard 754  section 4  This kind of rounding is sometimes called rounding to nearest  or banker s rounding  If digits is zero  this kind of rounding is sometimes called rounding toward zero

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Silverlight doesn t support the MidpointRounding option   Here s an extension method for Silverlight that adds the MidpointRounding enum   public enum MidpointRounding       ToEven      AwayFromZero    public static class DecimalExtensions       public static decimal Round this decimal d  MidpointRounding mode                return d Round 0  mode                   lt summary gt          Rounds using arithmetic  5 rounds up  symmetrical  up is away from zero  rounding          lt  summary gt           lt param name  d  gt A Decimal number to be rounded  lt  param gt           lt param name  decimals  gt The number of significant fractional digits  precision  in the return value  lt  param gt           lt returns gt The number nearest d with precision equal to decimals  If d is halfway between two numbers  then the nearest whole number away from zero is returned  lt  returns gt      public static decimal Round this decimal d  int decimals  MidpointRounding mode                if   mode    MidpointRounding ToEven                         return decimal Round d  decimals                     else                       decimal factor   Convert ToDecimal Math Pow 10  decimals                int sign   Math Sign d               return Decimal Truncate d   factor   0 5m   sign    factor                      Source  http   anderly com 2009 08 08 silverlight-midpoint-rounding-solution

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using a custom rounding  public int Round double value        double decimalpoints   Math Abs value - Math Floor value        if  decimalpoints  gt  0 5          return  int Math Round value       else         return  int Math Floor value

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Since Silverlight doesn t support the MidpointRounding option you have to write your own  Something like   public double RoundCorrect double d  int decimals        double multiplier   Math Pow 10  decimals        if  d  lt  0          multiplier    -1       return Math Floor  d   multiplier    0 5    multiplier       For the examples including how to use this as an extension see the post   NET and Silverlight Rounding

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This is ugly as all hell  but always produces correct arithmetic rounding   public double ArithRound double number int places      string numberFormat              numberFormat   numberFormat PadRight numberFormat Length   places           return double Parse number ToString numberFormat

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The default MidpointRounding ToEven  or Bankers  rounding  2 5 become 2  4 5 becomes 4 and so on  has stung me before with writing reports for accounting  so I ll write a few words of what I found out  previously and from looking into it for this post  Who are these bankers that are rounding down on even numbers  British bankers perhaps    From wikipedia  The origin of the term bankers  rounding remains more obscure  If this rounding method was ever a standard in banking  the evidence has proved extremely difficult to find  To the contrary  section 2 of the European Commission report The Introduction of the Euro and the Rounding of Currency Amounts suggests that there had previously been no standard approach to rounding in banking  and it specifies that  quot half-way quot  amounts should be rounded up   It seems a very strange way of rounding particularly for banking  unless of course banks use to receive lots of deposits of even amounts  Deposit   2 4m  but we ll call it   2m sir  The IEEE Standard 754 dates back to 1985 and gives both ways of rounding  but with banker s as the recommended by the standard  This wikipedia article has a long list of how languages implement rounding  correct me if any of the below are wrong  and most don t use Bankers  but the rounding you re taught at school   C C   round   from math h rounds away from zero  not banker s rounding  Java Math Round rounds away from zero  it floors the result  adds 0 5  casts to an integer   There s an alternative in BigDecimal Perl uses a similar way to C Javascript is the same as Java s Math Round

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The nature of rounding  Consider the task of rounding a number that contains a fraction to  say  a whole number  The process of rounding in this circumstance is to determine which whole number best represents the number you are rounding   In common  or  arithmetic  rounding  it is clear that 2 1  2 2  2 3 and 2 4 round to 2 0  and 2 6  2 7  2 8 and 2 9 to 3 0   That leaves 2 5  which is no nearer to 2 0 than it is to 3 0  It is up to you to choose between 2 0 and 3 0  either would be equally valid    For minus numbers  -2 1  -2 2  -2 3 and -2 4  would become -2 0  and -2 6  2 7  2 8 and 2 9 would become -3 0 under arithmetic rounding   For -2 5 a choice is needed between -2 0 and -3 0    Other forms of rounding   Rounding up  takes any number with decimal places and makes it the next  whole  number  Thus not only do 2 5 and 2 6 round to 3 0  but so do 2 1 and 2 2   Rounding up moves both positive and negative numbers away from zero  Eg  2 5 to 3 0 and -2 5 to -3 0    Rounding down  truncates numbers by chopping off unwanted digits  This has the effect of moving numbers towards zero  Eg  2 5 to 2 0 and -2 5 to -2 0  In  banker s rounding  - in its most common form - the  5 to be rounded is rounded either up or down so that the result of the rounding is always an even number  Thus 2 5 rounds to 2 0  3 5 to 4 0  4 5 to 4 0  5 5 to 6 0  and so on    Alternate rounding  alternates the process for any  5 between rounding down and rounding up    Random rounding  rounds a  5 up or down on an entirely random basis   Symmetry and asymmetry  A rounding function is said to be  symmetric  if it either rounds all numbers away from zero or rounds all numbers towards zero   A function is  asymmetric  if rounds positive numbers towards zero and negative numbers away from zero   Eg  2 5 to 2 0  and -2 5 to -3 0   Also asymmetric is a function that rounds positive numbers away from zero and negative numbers towards zero  Eg  2 5 to 3 0  and -2 5 to -2 0   Most of time people think of symmetric rounding  where -2 5 will be rounded towards -3 0 and 3 5 will be rounded towards 4 0   in C  Round AwayFromZero

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Firstly  this wouldn t be a C  bug anyway - it would be a  NET bug  C  is the language - it doesn t decide how Math Round is implemented   And secondly  no - if you read the docs  you ll see that the default rounding is  round to even   banker s rounding       Return ValueType  System DoubleThe integer nearest a  If the   fractional component of a is halfway   between two integers  one of which is   even and the other odd  then the even   number is returned  Note that this   method returns a Double instead of an   integral type       RemarksThe behavior of this method follows IEEE Standard 754    section 4  This kind of rounding 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    You can specify how Math Round should round mid-points using an overload which takes a MidpointRounding value  There s one overload with a MidpointRounding corresponding to each of the overloads which doesn t have one    Round Decimal    Round Decimal  MidpointRounding  Round Double    Round Double  MidpointRounding  Round Decimal  Int32    Round Decimal  Int32  MidpointRounding  Round Double  Int32    Round Double  Int32  MidpointRounding    Whether this default was well chosen or not is a different matter   MidpointRounding was only introduced in  NET 2 0  Before then I m not sure there was any easy way of implementing the desired behaviour without doing it yourself   In particular  history has shown that it s not the expected behaviour - and in most cases that s a cardinal sin in API design  I can see why Banker s Rounding is useful    but it s still a surprise to many   You may be interested to take a look at the nearest Java equivalent enum  RoundingMode  which offers even more options   It doesn t just deal with midpoints

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From MSDN      By default  Math Round uses   MidpointRounding ToEven  Most people   are not familiar with  rounding to   even  as the alternative   rounding   away from zero  is more commonly   taught in school   NET defaults to    Rounding to even  as it is   statistically superior because it   doesn t share the tendency of    rounding away from zero  to round up   slightly more often than it rounds   down  assuming the numbers being   rounded tend to be positive     http   msdn microsoft com en-us library system math round aspx

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I had this problem where my SQL server rounds up 0 5 to 1 while my C  application didn t  So you would see two different results   Here s an implementation with int long  This is how Java rounds   int roundedNumber    int Math Floor d   0 5     It s probably the most efficient method you could think of as well   If you want to keep it a double and use decimal precision   then it s really just a matter of using exponents of 10 based on how many decimal places   public double getRounding double number  int decimalPoints        double decimalPowerOfTen   Math Pow 10  decimalPoints       return Math Floor number   decimalPowerOfTen   0 5   decimalPowerOfTen      You can input a negative decimal for decimal points and it s word fine as well   getRounding 239  -2    200

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Here s the way i had to work it around    Public Function Round number As Double  dec As Integer  As Double     Dim decimalPowerOfTen   Math Pow 10  dec      If CInt number   decimalPowerOfTen    Math Round number   decimalPowerOfTen  2  Then         Return Math Round number  2  MidpointRounding AwayFromZero      Else         Return CInt number   decimalPowerOfTen   0 5    100     End If End Function   Trying with 1 905 with 2 decimals will give 1 91 as expected but Math Round 1 905 2 MidpointRounding AwayFromZero  gives 1 90  Math Round method is absolutely inconsistent and unusable for most of the basics problems programmers may encounter  I have to check if   int  1 905   decimalPowerOfTen   Math Round number   decimalPowerOfTen  2  cause i don not want to round up what should be round down

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Simple way is   Math Ceiling decimal Parse yourNumber

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From MSDN  Math Round double a  returns      The integer nearest a  If the   fractional component of a is halfway   between two integers  one of which is   even and the other odd  then the even   number is returned        and so 2 5  being halfway between 2 and 3  is rounded down to the even number  2    this is called Banker s Rounding  or round-to-even   and is a commonly-used rounding standard   Same MSDN article      The behavior of this method follows   IEEE Standard 754  section 4  This   kind of rounding 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    You can specify a different rounding behavior by calling the overloads of Math Round that take a MidpointRounding mode

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That s called rounding to even  or banker s rounding   which is a valid rounding strategy for minimizing accrued errors in sums  MidpointRounding ToEven   The theory is that  if you always round a 0 5 number in the same direction  the errors will accrue faster  round-to-even is supposed to minimize that   a    Follow these links for the MSDN descriptions of    Math Floor  which rounds down towards negative infinity  Math Ceiling  which rounds up towards positive infinity  Math Truncate  which rounds up or down towards zero  Math Round  which rounds to the nearest integer or specified number of decimal places  You can specify the behavior if it s exactly equidistant between two possibilities  such as rounding so that the final digit is even   Round 2 5 MidpointRounding ToEven   becoming 2  or so that it s further away from zero   Round 2 5 MidpointRounding AwayFromZero   becoming 3     The following diagram and table may help   -3        -2        -1         0         1         2         3   -- ------ --------- ---- ---- -- ------ ---- ---- ------- -      a                     b       c           d            e                         a -2 7  b -0 5  c 0 3  d 1 5  e 2 8                                                            Floor                    -3      -1      0      1      2 Ceiling                  -2       0      1      2      3 Truncate                 -2       0      0      1      2 Round ToEven             -3       0      0      2      3 Round AwayFromZero       -3      -1      0      2      3   Note that Round is a lot more powerful than it seems  simply because it can round to a specific number of decimal places  All the others round to zero decimals always  For example   n   3 145  a   System Math Round  n  2  MidpointRounding ToEven            3 14 b   System Math Round  n  2  MidpointRounding AwayFromZero      3 15   With the other functions  you have to use multiply divide trickery to achieve the same effect   c   System Math Truncate  n   100    100                        3 14 d   System Math Ceiling  n   100    100                         3 15      a  Of course  that theory depends on the fact that your data has an fairly even spread of values across the even halves  0 5  2 5  4 5       and odd halves  1 5  3 5         If all the  half-values  are evens  for example   the errors will accumulate just as fast as if you always rounded up

[.net] Why does Math.Round(2.5) return 2 instead of 3?

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