Unit I Reading:
Significant Figures
Laboratory investigations usually involve the taking of and interpretation of measurements.
All
physical measurements obtained by
means of instruments (meter sticks, thermometers,
electrical meters, clocks, etc.)are to some extent uncertain.
If, for example, the mass of an
object is determined by means of a DialOGram balance, the measured mass will be uncertain
by at least
+
0.01 gram.
If the object were now weighed on progressively more accurate scales,
the uncertainty in the mass of the object would get progressively less, but regardless of the
precision of the measuring device, any instrumental measurement is to some extent uncertain.
The degree of uncertainty in physical measurements can be indicated by means of significant
figures.
Consider, for example, a measurement of the length of the object as indicated below, with three
differently calibrated meter sticks.
Figure 1
Observe that when measuring the length of the object with the uncalibrated meter stick (top)
the actual length of the object in Figure 1 can only be estimated, and then only to the nearest
tenth of a meter, or as 0.3 meter (one significant figure).
Measuring the length of the object, however, with a meter stick calibrated in tenths of a meter
(center stick in Figure 1) it is obvious that the length of the object is greater than 0.2 m but less
than 0.3 m.
Once again, it would seem to be reasonable to estimate the length of the object to
the nearest tenth of the smallest calibration or to the nearest hundredth of a meter; thus 0.27 m.
It might actually be as short as 0.26 m or as long as 0.28 m, so 0.27 m (to the nearest hundredth
of a meter) seems to be the most reasonable estimate of the object's length.
This measurement
has two significant figures indicating less uncertainty in the second measurement than in the
first.
Measuring the length of the object with a meter stick calibrated in hundredths of a meter (lower
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 Fall '11
 Dr.LairdKramer
 0.269 M, 0.02 g, 0.270 M, 0.271 M

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