11.3 Handling Errors
167
When adding or subtracting two values x and y and their errors x and y to
find z, the error in the resultant value z is given by
z =
((x) 2 + ((y) 2 .
(11.6)
For the multiplication of two values, the propagated uncertainty is
z = |x y|
x
x
2
+
y
y
2
.
(11.7)
For the division of two values, the propagated uncertainty is
z =
x
y
x
x
2
+
y
y
2
.
(11.8)
When raising a result x to a power n, the error in the result z is given by
z = |n| x
n−1
x.
(11.9)
When applying a function f to x and y, the propagated error is given by
z =
δ f
δx
+
δ f
δy
(y)
2
.
(11.10)
167
When adding or subtracting two values x and y and their errors x and y to
find z, the error in the resultant value z is given by
z =
((x) 2 + ((y) 2 .
(11.6)
For the multiplication of two values, the propagated uncertainty is
z = |x y|
x
x
2
+
y
y
2
.
(11.7)
For the division of two values, the propagated uncertainty is
z =
x
y
x
x
2
+
y
y
2
.
(11.8)
When raising a result x to a power n, the error in the result z is given by
z = |n| x
n−1
x.
(11.9)
When applying a function f to x and y, the propagated error is given by
z =
δ f
δx
+
δ f
δy
(y)
2
.
(11.10)