Errors When Subtracting

Fred expressed some confusion and concern about the results he received when subtracting certain numbers. For instance, when he subtracts 3809717.98 from 3799904.94, he should get -9813.04, but instead gets -9813.04000000003.

What Fred is witnessing is an artifact of Excel's limitations. The problem is ultimately related to how Excel works with floating-point numbers. Computers must store numbers internally as binary values, not as the decimal values we see displayed on the screen. Whole numbers can be stored as binary values relatively easily. When you throw a decimal point into the mix, then storing very large or very small numbers becomes more problematic—Excel just isn't able to store them with absolute precision. Instead, Excel provides an "approximate" result, out to 15 digits (the limits of its precision). Thus, you end up with something like -9813.04000000003, which contain the full 15 digits of precision possible in Excel.

A full discussion of how floating-point numbers are maintained in Excel and computers in general can very quickly get extremely technical. For those who want more information on the topic, here are two places you can start your research:

http://support.microsoft.com/?kbid=78113
http://docs.sun.com/source/806-3568/ncg_goldberg.html

The bottom line is that the only way to get the "exact" results you want, to the number of decimal places you want, is to use the ROUND function in your formulas, as shown here:

=ROUND(3799904.94 - 3809717.98, 2)

You can also, if desired, change the precision used to within all formulas by following these steps:

1. Choose Options from the Tools menu. Excel displays the Options dialog box.
2. Make sure the Calculation tab is displayed. (Click here to see a related figure.)
3. Ensure that the Precision As Displayed check box is selected.
4. Click OK.

In Excel 2007 you would follow these steps:

1. Click the Office button and then click Excel Options. Excel displays the Excel Options dialog box.
2. At the left of the dialog box click Advanced.
3. Scroll through the available options until you get to the section entitled "When Calculating this Workbook." (Click here to see a related figure.)
4. Ensure that the Set Precision As Displayed check box is selected.
5. Click OK.

Now, Excel uses the precision shown on the screen in all of its calculations, instead of doing calculations at the full 15-digit precision it normally maintains.