More sophisticated ways exist to handle uncertainties in quantities than significant figures.
[For an
extensive discussion, see the NIST website on
Uncertainty of Measurement Results
.]
However,
using this relatively simple formalism should create a sensitivity and appreciation for the connections
between measuring devices, their capabilities, and their limitations. Many exercises involve the
determination and reporting of some quantitative property. Both the value of the property and its
uncertainty will be important. It is essential that each measurement that leads to the value has been
made with the full capability of the devices and apparatus used in its determination.
SUPL001
contains a brief section on the concept of
significant figures
. As noted in that supplement:
•
close attention will be paid to the use of significant figures in laboratory reports
•
grading standards for exercises and quizzes invariably include a substantial number of points
that deal with the proper implementation of this concept.
•
you are urged to master this concept early in the laboratory course.
We encourage the use of electronic calculators for facilitating the computations associated with
experimental numbers, but, even inexpensive calculators are designed to deal with, and display,
numbers having 10 or more digits. This places the burden of accounting for the appropriate
representation of numerical data on the student investigator.
•
everyday laboratory measurements limit the number of digits that represent
reality
•
the concept of
significant figures
seeks to limit the number of digits in a quantity to those that
are justified based on its origin
Two features play a role in the determination of significant figures 
measurement
, and
computation
using measured values.
Measurement:
•
for a quantity that is the result of a direct measurement, the number of
decimal digits
(the
number of digits in the representation of the number, both to the right and the left of the
decimal point) in that quantity is generally fixed by the measuring device. The number of
significant digits
can depend on the value of the measurement.
•
Our
rule of thumb
is that, for a device whose output is
linear
, the eye can estimate values
lying between two marks on a scale to onefifth of the distance between the two marks.
For experimentally determined quantities, the number of significant figures is
not
simply related to the
intrinsic precision
of a device. Consider the buret and the analytical balance.
The
buret
permits a volume to be read to ± 0.02 mL (onefifth of the smallest division on its scale).
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 Spring '08
 ROBERTSCHNEIDER
 Chemistry, pH, Decimal, investigator

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