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Precision
Significant Figures
Significant figures are the number of digits required to express the accuracy of a particular
measurement or the accuracy of a calculation involving measurements. As a general rule one
assumes uncertainty in only the last digit and all other digits are considered to be certain or
definite.
Consider the measurement of the same solid rod using two different rulers. RULER 1 has
graduations (marks) every 1/10 of a cm (i.e. every millimeter). RULER 2 has graduations every
centimeter. Assume the left end of the rod and the metric rulers (not shown in the figure) are
aligned perfectly. The length of the rod in centimeters is obtained by reading the rulers at the right
end of the rod and estimating the last “digit”. The rulers enlarged for clarification and are not
depicted to scale. That is the centimeter shown is not actually a centimeter in length.
Let us examine what the reading for length would be for each ruler.
Ruler 1
Ruler 2
1. Length is definitely between 4 and 5 cm.
1. Length is definitely between 4 and 5
cm.
2. Length is definitely between 4.4 and 4.5
cm.
2. Estimate length is around 4.5 cm.
3. Estimate length between 4.47 and 4.49
cm.
3. Report length as 4.5 ± 0.1 cm.
4. Report length as 4.48 ± 0.01 cm
In each measurement there was but one uncertain digitthe last estimated digit. Regardless
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View Full DocumentRULER 1 produced the more precise measurement. The value of length utilizing RULER 1 has
three “significant figures” while the value of length obtained utilizing RULER 2 has two
“significant figures”. Generally for a given measurement, the value with the larger number of
“significant figures” is the more precise value.
Ruler 1 allows measurements to ± 0.01 cm. Consider a different rod again with the left end of both
the rod and ruler perfectly aligned. If the right end of the rod is exactly over the graduation at 3.8,
the length of the rod would be reported as 3.80 ± 0.01 cm. The number of significant figures is
three with uncertainty found only in the last digit which is zero. This example illustrates the fact
that zeros after decimal points are significant. Of course, nonzero digits are always significant in
this type of measurement.
Generally the numerical value of a measured quantity is reported to only one uncertain figure. The
number of digits in the number is called the number of significant figures. One can assume that
the nonzero digits of an experimental measurement are significant. With this assumption, rules
have been devised to understand whether a zero (0) in a number is significant or not.
Significant Figures in a Measurement
1.
The significance of zero and nonzero digits in a number.
(a)
Assume nonzero digits are significant.
(b)
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 Fall '10
 Borovick

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