All about ROUNDING

Introduction

ROUNDING is a very important factor in Mathematical calculations. In MS SQL Server we offend use different function to round the mathematical data. I saw that developer face a common problem when rounding data. It may be mathematical rounding or financial rounding. The main cause of facing problem, it is not to shame to say a lot of developer doesn't have any idea about rounding and how it works. In this article I am trying to clear all the problem related to rounding. Hope you like it and find it useful.

Tropics to discuss

1.    What the Logic Behind Rounding

2.    MS SQL Server and Rounding

3.    Financial Rounding

What the Logic Behind Rounding

As I am not a mathematician, so I follow some simple rules for mathematical rounding.

1.    If the last digit is less than 5 – you must drop it.

2.    If the last digit is greeter then 5 – you must drop it and increase the second to last digit by 1.

3.    If the last digit is equal to 5 -- drop the five and increase the second to last digit by one if it is odd, and do not increase the second to the last digit if it is even.

If we take an example

1.    Rounding 12.71   =   12.7

2.    Rounding 12.79   =   12.8

3.    Rounding 12.75   =   12.8   and Rounding 12.85  =  12.8  

MS SQL Server and Rounding

In MS SQL Server the rounding function depends on the data type.

Depends upon the data type (Int, float, decimal etc) the rounding value may be different. The MS SQL Server provide 3 types of rounding functions ROUND(), CEILING() and FLOOR() and depends on the function the value is different.

ROUND()

It returns a numeric value and round up to specified length or precisions.

The syntax is

ROUND ( numeric_expression , length [ ,function ] )

Numaric_Expressions

This can be positive or negative numbers and data type can be Int, decimal, numeric, money or small money.

If the length is an negative number in this case

Example	Result
ROUND(748.58, -1)	750
ROUND(748.58, -2)	700
ROUND(748.58, -3)	Numeric Over flow

In this Example of ROUND() the Last digit is always estimated

Example	Result
ROUND(123.9994, 3)	123.9990
ROUND(123.9995, 3)	123.0000

In this Example of ROUND() Showing approximations

Example	Result
ROUND(123.4545, 2)	123.4500
ROUND(123.45, -2)	100.00

In this Example of ROUND() Showing round and truncation

Example	Result
ROUND(150.75, 0)	151.00
ROUND(150.75, 0, 1)	150.00

CEILING()

Evaluates the value on the right side of the decimal and returns the smallest integer greater than, or equal to, the specified numeric expression. It accepts one value (Value to round).

Example:

SELECT CEILING(123.45) AS 'CEILING(123.45)',

       CEILING(-123.45)AS 'CEILING(-123.45)',

       CEILING(0.0)    AS 'CEILING(0.0)'

CEILING(123.45)       CEILING(-123.45)      CEILING(0.0)

124                              -123                             0

FLOOR()

Evaluates the value on the right side of the decimal and returns the largest integer less than or equal to the specified numeric expression and accepts one value (Value to round).

SELECT FLOOR(123.45) AS 'FLOOR(123.45)',

       FLOOR(-123.45)AS 'FLOOR(-123.45)',

       FLOOR(0.0)    AS 'FLOOR(0.0)'

FLOOR(123.45)         FLOOR(-123.45)        FLOOR(0.0)

123                              -124                             0

Financial Rounding

If I have a fanatical report showing

Srl. No	Description	Amount in Rs
1	Item-1	1000.15
2	Item-2	1000.25
3	Item-3	1000.35
4	Item-4	1000.45
Total		4001.20

If you say a customer to pay Rs. 4001.20 you definitely get some …..

So it should be rounded up to Rs. 4001.00. In another example if the grand total is Rs. 4001.71, it should be rounded up to Rs. 4002.00.

To get this type of rounding we can make an UDF of MS SQL Server. Here we are taking a concept of Round off (+) or Round off (-).

IF OBJECT_ID('dbo.fn_finantialRound') IS NOT NULL

   BEGIN

     DROP FUNCTION dbo.fn_finantialRound;

   END

GO

CREATE FUNCTION fn_finantialRound

(

      @p_RoundNumber DECIMAL(20,2)

)

RETURNS DECIMAL

AS

BEGIN

      DECLARE @v_RerVal   DECIMAL(20,2),

              @v_RndZero  DECIMAL(20,2),

              @v_OrgNo    DECIMAL(20,2),

              @v_StoreVal DECIMAL(20,2);

     

      SET @v_OrgNo    = @p_RoundNumber;

      SET @v_RndZero  = ROUND(@p_RoundNumber, 0);

      SET @v_StoreVal = @v_RndZero - @v_OrgNo;

     

      IF @v_StoreVal > 0

         BEGIN

            SET @v_RerVal = @v_OrgNo + @v_StoreVal;

         END

      ELSE IF @v_StoreVal < 0    

              BEGIN

                 SET @v_RerVal = @v_OrgNo - ABS(@v_StoreVal);

              END

           ELSE

              BEGIN

                 SET @v_RerVal = @p_RoundNumber;

              END  

     

      RETURN @v_RerVal;

END

GO

-- Testing

SELECT dbo.fn_finantialRound(12.27) -- 12.00

SELECT dbo.fn_finantialRound(12.77) -- 13.00

  

Hope you like it.

Posted by: MR. JOYDEEP DAS