SQL Server : SUM() weird behaviour

Question

I run this example in SQL Server Management Studio:

SELECT CONVERT(REAL, -2101.12) n INTO #t
SELECT * FROM #t
SELECT SUM(n) FROM #t

The first SELECT creates a temp table #t with 1 column n of type real, and it puts 1 row in it with the value -2101.12.

The second SELECT confirms that the table is created with the intended content and the result is:

n
---------
-2101.12

The third SELECT sums the only number that is there, but the result is:

-2101.1201171875

So the question is: Where the 0.0001171875 comes from?

EDIT: I know the lack of precision for the real and float data types, unfortunately I cannot change the database schema because of this. What surprise me though, is that I would expect to see also the extra decimals in the second select since it is supposed to be stored with that lack of precision. Since it does not happens on the second select, then why the sum function picks it up?

Answer 1

You've just discovered real (aka floating point) data is approximate. Use decimal datatype instead.

Answer 2

The FLOAT and REAL data types are known as approximate data types. The behavior of FLOAT and REAL follows the IEEE 754 specification on approximate numeric data types.

Approximate numeric data types do not store the exact values specified for many numbers; They store an extremely close approximation of the value. For many applications, the tiny difference between the specified value and the stored approximation is not noticeable. At times, though, the difference becomes noticeable. Because of the approximate nature of the FLOAT and REAL data types, do not use these data types when exact numeric behavior is required, such as in financial applications, in operations involving rounding, or in equality checks. Instead, use the integer, decimal, money, or smallmoney data types.
Avoid using FLOAT or REAL columns in WHERE clause search conditions, especially with the = or <> operators. It is best to limit FLOAT and REAL columns with > or < comparisons.

Source of above statement