The question of the number of significant figures is part of the
general problem of interpreting the results of measurements.
In this regard, my pet stance is that the precision is not just
a question of how finely divided is the scale of the instrument.
THE METHOD OF MEASUREMENT IS ALSO VERY IMPORTANT. To show this I
have invented the following short story:
A teacher gives a box of cigarettes to three students and requests them
to measure the lenght of a cigarette. The only instrument they can
use is a ruler whose marks are spaced one meter apart.
The students report their work as follows:
JOSEPH: the cigarette is a lot shorter than 1 meter.
DAVID : the length of the cigarette is 0 plus or minus 0.5 meter.
ROSE: the length of the cigarette is between 1/13 and 1/12
meters, that is between 7.7 and 8.3 cm.
Rose explanation: 1) I noticed that all the cigarettes in my box
have aprox. the same length.
2) Putting several cigarettes on line (end by end)
close to the ruler, it is seen that 12 cigarettes
are a little less than 1 meter, while 13 cigarettes
are a little more than 1 meter.
My comments: -- Perhaps Joseph is lazy, but he did not lie!
-- David is just following an old (AND FALSE) advice. It
not true that "the error is equal to one half of the
smallest division of the scale". The instruments do
not HAVE errors. Sometimes WE commit errors when we
use them.
-- I would like to have more students like Rose!
Even if it is not forbidden to use their brains,
only Rose does.
-- Giving an informal "interval of confidence" for the
length of the cigarette is a very good practice before
more sophisticated data analysis.