Why is zero showing as a negative value?

Question

Does anyone know why zero is showing as a negative value?

Answer 1

Hi Neil,
Not really a bug, just a limitation of the mathematics involved.
You're entering the numbers as base 10 numerals. Computers work in base 2, so before any calculation is done, each number must be converted to its base 2 representation.
All of the calculations are done in base 2, then the results are presented as base 10, rounded to whatever precision you have set (or the defaut precision for currency amounts—to the nearer hundredth of the base unit). What you see is a rounded value, but what is actually in the cell is the result of the calculation, including the rounding errors inherent in the process.
Those errors arise from a simple fact: Not all numbers in base 10 can be expressed exacty in base 2. (Not all numbers can be expressed exactly in base 10 either, but that's a different discussion.) Expression of numbers in the math underlying Numbers is accurate to 15 places (base 10), regardless of which side of the decimal point those places occur.
Each of the "zeros" in your sums involves several pieces of data in the sum, not all of which can be expressed exactly in base 2. In two of the sums, the errors (if any) cancel out and there is no difference between the sum expressed to two decimal places and the same sum expressed to 15 digits. In the other three, this is not true, as can be seen below.
The image is of your test table. Columns A, B, and C have been reduced i width, all non-sum rows have been hidden to reduce the image size, and the SUM cells have been set to show 30 places (the maximum permited in Numbers) after the decimal to ensure that all significant places are shown, and that the decimal points are lined up for easy comparison.
Note that three of the results differ from their displayed (two decimal place) values. The largest difference is in the third value, the smallest in the forth. The absolute difference between expected and actual result in the third of these lies between the other two, but is more noticeable because the result is less than zero and carries the - sign because of that. The minus sign is not "inserted" (randomly) by the software; it's there for the same reason there's a minus sign in the cell containing -103.31 is in that cell: the value in the cell is negative.
"If I replace the cells containing the duplicates eg. £269.57, £90.11 & £103.31 with numbers manually added together £539.14, £180.22, £206.62. - the software doesn't insert the negative."
Nor does it "insert the negative" in the first cell displaying a "zero" result, or the cell displaying a 26.04 result. Replacing those six numbers with six (or three) others changes the translation errors for each of these pieces of the sum, and that changes the sum itself. In this case the cumulative error moved the result from being 'smaller' than expected to 'larger' than expected. The result is now slightly larger than zero, so the minus sign is not needed or appropriate.
Here are two further examples. The sum shown is the one in row 130. The data is the same as in the original table except for rows 126 and 127.
Original values:
Two occurrences of -90.11 replaced with a 0 and -180.22 produced this change in the result. Still negative, so the minus sign wi still be there.
Two occurrences of -90.11 replaced with -90.10 and 90.12:
A surprise! The actual value is zero (to the limits of precision of the underlying math).
But that's not (for the usual user) a predictable result.
Depending what you are doing with the results, you may want to do the rounding proposed by Wayne. This will change the actual vaue in the cell to the displayed value ( 0.00), and will remove the minus sign.
It's not a bug—Numbers follows ISO standards in its math—but you may wish to Provide Numbers Feedback to Apple regarding your (and others) user expectations. You'll find an item with that name in the Numbers menu in Numbers.
Regards,
Barry