 |
 |
31 of 36 |  |
 |
 |
31
Thus the relative error (i.e. percent uncertainty)
is:
Percent uncertainty
=
error
in
volume
measurement
volume
x
100
%
=
0.10 mL
2.25 mL
x 100% = 4.4%
B.
Significant Figures
The rules for the use of significant figures
are useful approximations to a full use of the rules for
propagation of errors.
1.
Addition and Subtraction
The number of significant figures to the
right of the decimal point in the sum or difference is equal to
the smallest number of figures to the
right of the decimal point.
Example #1: Add three numbers
0.168
10.784
15.16
26.112
The answer to the correct number of significant
figures is 26.11 (two significant figures to the
right of the decimal point).
Example #2: Add the three numbers
1.05 x 10
-10
, 2.01 x 10
-11
, and 5.03 x 10
-12
. First, all three
numbers have to be converted to a common
power of 10, for example, 10
-11
(any common
power will do):
10.5
x 10
-11
2.01
x 10
-11
0.503
x 10
-11
13.013
x 10
-11
The answer to the correct number of significant
figures is 13.0 x 10
-11
(one significant figure to the right
of the decimal point in the common power of
10
-11
). In addition and subtraction,
the answer should be expressed to the same degree of
uncertainty contained in the least precise
measurement (least number of decimal places).
