Why is this simple Excel calculation not netting Zero?

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It's supposed to be zero but for some reason the result produces a peculiar series of digits at the end.

Also, here's the .xlsx of it: http://83.212.111.36/Book1.xlsx

j riv

Posted 2013-04-06T10:43:31.153

Reputation: 2 162

I found a workaround with round(), and I heard it's a problem with floating arithmetic. I do not know if it can be fixed. – j riv – 2013-04-06T11:00:13.820

Answers

This happens because of the limited precision of floating point numbers representation on computers and cannot be fixed because it is an intrinsic problem of the way number are represented on a computer. There might be workarounds, such as round() or a clever implementation of the formulas to reduce error propagations.

Excel uses 8-byte (64 bit) floating point representation, meaning that it can achieve a maximum accuracy of about 10^-15. The inaccuracy can then spread across the steps of a calculation.

I suggest that you read this article on Wikipedia that investigates this topic.

Pincopallino

Posted 2013-04-06T10:43:31.153

Reputation: 947

They were using floating point on the windows calculator too to aquire new and different math :-) Simple rounding could have solutioned it. Instead I get to read 20 pages of stuff about it to find out that FP has a specific accuracy as used, and within that accuracy used, it should just be rounded back to within that accuracy. Rounded proper not chopped. – Psycogeek – 2013-04-06T12:40:09.200

Advanced users may decide if they need a rounded or truncated result based on their needs. Unnecessary rounding slows down the calculations. – Pincopallino – 2013-04-08T14:04:19.463

Self post: It's a documented limitation for floating point arithmetic: http://support.microsoft.com/kb/78113

IMO it should be warning more visibly when the results can be so blatantly erroneous to not be considered a bug, but anyway.

A workaround is to use round().

j riv

Posted 2013-04-06T10:43:31.153

Reputation: 2 162