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Since you now know how to determine the number of significant
figures in a quantity and to give the result of a calculation
in the correct number of significant figures, we
can expand our discussion to include the correct number of significant
figures in measurements.
A significant figure is one that has some significance but
does not necessarily denote a certainty. Whenever
you estimate any kind of measurement, for example the length
or weight of an object, there is always a limit to the number
of digits you can read.
The number of significant figures
in a measurement is the number of digits that are known with
certainty plus the last one that is not absolutely certain.
A length measurement of 5.63 contains three significant figures.
The first two, the 5 and 6, are certain. The least, the 3, is
uncertain. The uncertainty in the last significant figure is
usually + 1. Therefore the result is 5.63 + 0.01cm.
An Analytical Balance is precise
to four decimal places with an uncertainty of +1 in the last
significant figure. Therefore, the measurement is
13.7654g is written as 13.7654 + 0.0001 g and has six
significant figures.
BURET
Here we see another kind of measurement, the reading of the position
of a buret meniscus, (the curved liquid surface in a buret).
The liquid level is always read at the bottom of the meniscus
for transparent liquids. The reading in this buret is 12.75; four
significant figures are implied. The
last significant figure, 5, is obtained by visual interpolation
between the 0.1 milliliter divisions. All observers
should agree with the first three significant figures but not
necessarily with the last figure recorded here. Disagreements
of +1 in the last digit are expected with visual interpolations.
Therefore, the measurement is written as 12.75 + 0.01ml
and has four significant figures.
METER
When reading a measurement from a meter, you should also read to one digit past the smallest division
on the meter. On this meter, the reading should
be 1.27. The 1 and the 2 are certain. The 7 must be estimated
visually. Therefore the measurement is written as 1.27 +
0.01g.
As a general rule you should attempt
to read any scale to one tenth of its smallest division by visual
interpolation, in this case to + 0.01cm.
This estimated figure will always be your last significant figure
with the implied accuracy of + 1. Therefore, the measurement
is written as 4.63 + 0.01cm.
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