EXPERIMENT 2.
MEASUREMENT AND PRECISION
your measured value as
x
0
±
δx
where
x
0
is the average value from your measurements and
δx
is called the uncertainty and is half the deviation from the largest to smallest measured
values.
Note that the number of significant figures you include in your results is limited by the
number of significant figures in the least precise measurement in your data. Suppose you
measured the circumference to be
c
= 508 mm (which has 3 significant figures) and you
measured the diameter to be
d
= 148 mm (which also has 3 significant figures). According
to your calculator, the ratio
c
/
d
is equal to 3.432432432. This has 10 significant figures! You
must round off this answer to three significant figures and write
c
/
d
=3.43.
Numbers containing too many significant figures are wrong because they imply a precision
that is not justified by your measurements! For the same reason quantities calculated from
measured values that do not include the uncertainty are wrong. To reiterate, your final result
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 Fall '08
 Staff
 Physics, Δx

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