Why when I save a value of say 40.54 in SQL Server to a column of type Real does it return to me a value that is more like 40.53999878999 instead of 40.54? I've seen this a few times but have never figured out quite why it happens. Has anyone else experienced this issue and if so causes it?
+8
A:
Floating point numbers use binary fractions, and they don't correspond exactly to decimal fractions.
For money, it's better to either store number of cents as integer, or use a decimal number type. For example, Decimal(8,2) for numbers of the form xxxxxxxx.xx, i.e. to cent precision.
Javier
2008-11-07 19:42:30
I'd love to have both of you get the points for answering well. Instead of storing the cents we are using themoney value. Do you think that this is also a good practice?
Middletone
2008-11-07 19:48:17
Storing the cents is bad news. Financial institutions often use fractional cents in calculations, and sometimes need to store them as well. I was on a project once where this came up after the cents-storing app was deployed. Very ugly.
MusiGenesis
2008-11-07 20:08:57
+20
A:
Have a look at What Every Computer Scientist Should Know About Floating Point Arithmetic.
Floating point numbers in computers don't represent decimal fractions exactly. Instead, they represent binary fractions. Most fractional numbers don't have an exact representation as a binary fraction, so there is some rounding going on. When such a rounded binary fraction is translated back to a decimal fraction, you get the effect you describe.
For storing money values, SQL databases normally provide a DECIMAL type that stores exact decimal digits. This format is slightly less efficient for computers to deal with, but it is quite useful when you want to avoid decimal rounding errors.
Greg Hewgill
2008-11-07 19:42:53
+3
A:
In a nutshell, it's for pretty much the same reason that one-third cannot be exactly expressed in decimal. Have a look at David Goldberg's classic paper "What Every Computer Scientist Should Know About Floating-Point Arithmetic" for details.
Sherm Pendley
2008-11-07 19:44:31
+1
A:
To add a clarification, Most floating point numbers stored in computers behave as described by other posts here, because as described, they are stored in Binary... This means that unless their value (both the mantissa and exponent) are powers of two, they cannot be represented exactly.
Some systems, otoh, store floating point numbers in Decimal (SQL Server Decimal, and Numeric data types, and Oracle Number datatype for example,) and then their internal representation IS exact for any number that is a power of 10, and will be inexact for numbers that are not powers of 10.
Charles Bretana
2008-11-07 20:27:12