Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] Significant figures -- again



On 03/12/2012 09:27 AM, Paul Lulai wrote:
I've found that stating in terms of what they can measure or make
helps a bit. When a kid gives me an answer of 3.8675309 cm (or
anythings), I ask them if they could cut a board to that length. It
seems that they are less comfortable making something a certain
length (or weight etc...) than they are measuring to that precision.
Meaning if you give a 9th grader (or 12th grader, and I assume
college kid) a board to measure, they are happy to claim it is
3.8675309 cm long. Asking them to cut a board to that length makes
them think a bit more about what is appropriate.


I still think it is a Bad Idea to endorse -- explicitly or implicitly --
the idea that the number of digits tells you anything about the
uncertainty, tolerance, significance, or anything else.

Cutting a board to 3.8675309 ± 0.5 cm is not particularly difficult.
Cutting a board to 3.8675309 ± 0.0000005 cm is quite a bit more difficult.

The number of digits is at least two jumps removed from the main thing
folks ought to be focused on.
-- The number of digits might OR MIGHT NOT tell you about the
roundoff error.
-- The roundoff error might OR MIGHT NOT be the dominant contribution
to the overall uncertainty,

In a well-designed experiment, roundoff error will never be the dominant
contribution to the overall uncertainty. The idea of rounding off a
number until the roundoff error becomes comparable to (or the cause of)
the total uncertainty is sheer madness.

People who care about their data do not use sig figs.

The nominal value e.g. 3.8675309 cm is one number.
The uncertainty e.g. 0.5 cm is another number.

My recommendation: If you ever feel you need to use a single decimal
numeral to represent these two numbers, lie down until the feeling goes
away.

If a student writes down 3.8675309 cm, do not complain about what is
present (lots of digits), but rather complain about what is absent (any
explicit statement of the uncertainty).

Or ... don't complain at all. Sometimes it is entirely appropriate to
write down a number without knowing the uncertainty.
-- When I write a number with N digits, it does *NOT* imply anything
about the uncertainty. If I wanted to express the uncertainty I
would have expressed it explicitly.
-- Writing down more digits than are needed incurs a very small cost.
-- Writing down fewer digits than are needed sometimes incurs a very
very very large cost.