Rounding figures?

Subject: Rounding figures?
From: "Hart, Geoff" <Geoff-H -at- MTL -dot- FERIC -dot- CA>
To: "TECHWR-L" <techwr-l -at- lists -dot- raycomm -dot- com>
Date: Tue, 13 Mar 2001 13:18:37 -0500

Elizabeth Cummings reports: <<All the reports show figures that, at the
maximum, extend to one decimal point--but most show only figures that are
whole numbers. To the layperson's eye, some of these figures don't appear to
add up, and I understand from the development side that this is due to
rounding (e.g., On one report, column A shows "4" and column B shows "2",
and these two columns should add up to the sum shown in column C, which is
"7". In this situation, "4" was really 4.3, and "2" was really 2.3--the sum
of which of course rounds up to 7.).>>

Our practice (at FERIC) is twofold: to ensure that we present meaningful
numbers of numbers <g>, and that the totals add up. You wouldn't believe how
much time I spend correcting errors in addition and long division that
resulted from rounding! And yes, our readers notice these errors, so we make
it a priority to fix them.

That being the case, we begin by deciding how many digits are truly
meaningful to the reader, and round all numbers to that number of digits.
Once that's done, we recalculate all totals (plus averages, multiplication
results, etc.) to ensure that they add up with the new, rounded numbers; our
logic is that if the reader sees that simple calculations are clearly in
error, they're not going to trust any of our other conclusions either, and
they pay us a good deal of money for reliable conclusions. Where we
calculate the end result to many digits (e.g., in a spreadsheet) and the
accuracy or precision of that result is sufficiently important to present
that many digits to the reader, the results obviously won't add up if we
round the numbers that produce those results. So instead, we "unround" them
and present numbers with more digits than the reader strictly needs, but
that produce the right calculation results.

In the rare cases where we have to use both rounded numbers and a
calculation result that differs from these numbers, we always include a
footnote to the effect that "totals may not equal 100 as a result of
rounding errors". But that's rare. In your case, there are two equally
simple solutions: either present all numbers to one decimal place, or
present them to different numbers of decimal places and tell the reader that
the results are correct, even if the inputs don't suggest this is the case.
I dislike the second solution, since it both misleads the user ("hey, the
inputs say 2+2 but the answer is 5!") and adds the need for readers to
understand the plumbing of the software, when all they're really interested
in is the results of the calculation. Adding that complexity when you could
avoid it easily by fixing how the numbers are displayed strikes me as a bad

--Geoff Hart, FERIC, Pointe-Claire, Quebec
geoff-h -at- mtl -dot- feric -dot- ca
"User's advocate" online monthly at

"Arthur C. Clarke had suggested that any sufficiently advanced technology
would be indistinguishable from magic--referring to a possible encounter
with an alien civilization--but if a science journalist had one
responsibility above all else, it was to keep Clarke's Law from applying to
human technology in human eyes."--Greg Egan, "Distress"


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