PROPAGATION OF ERROR
Frequently it is necessary to combine measurements using some defined relation
to obtain a property of interest. For example, a measurement of mass of an
object may be combined with a measurement of its volume to determine its
density. As described earlier, a measurement consists of a best estimate and an
indication of its precision or uncertainty, x
±
s. When measurements are
combined, it is also necessary to combine their uncertainties, but in a specified
manner. Table 1 summarizes the common math operations and the specified
manner in which their uncertainties are to be combined.
Operation
z
Including uncertainties
s
z
Addition
z = x + y
(x
±
s
x
) + ( y
±
s
y
) = z
±
s
z
s
z
=
s
x
2
+
s
y
2
Subtraction
z = x  y
(x
±
s
x
)  ( y
±
s
y
) = z
±
s
z
s
z
=
s
x
2
+
s
y
2
Multiplication
z = x * y
(x
±
s
x
)*( y
±
s
y
) = z
±
s
z
s
z
z
=
s
x
2
x
2
+
s
y
2
y
2
Division
z = x / y
(x
±
s
x
)/( y
±
s
y
) = z
±
s
z
s
z
z
=
s
x
2
x
2
+
s
y
2
y
2
Exponential
z = x
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 Summer '11
 Bonk
 Accuracy and precision, Significance arithmetic

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