After going through the absolute error and the maximum absolute error, we face yet another type of error: accumulated error.
Accumulated error in computation
edit
Accumulated error in measurement
edit
Accumulated error is the maximum absolute error of a measurement which is obtained by using a formula which utilises approximate measurements. Take a look at this example for instance.
Example 1
Question
The length of a side of a square is 10cm long. Find the accumulated error of the area of the square.
Solution
The maximum absolute error of the length of the square:
{\displaystyle {\text{The maximum absolute error of the length of the square:}}\,}
=
1
cm
2
{\displaystyle ={\frac {1{\text{cm}}}{2}}}
=
0.5
cm
{\displaystyle =0.5{\text{cm}}\,}
The measured area of the square:
{\displaystyle {\text{The measured area of the square:}}\,}
=
10
2
cm
2
{\displaystyle =10^{2}{\text{cm}}^{2}\,}
=
100
cm
2
{\displaystyle =100{\text{cm}}^{2}\,}
The maximum area of the square:
{\displaystyle {\text{The maximum area of the square:}}\,}
=
(
10
+
0.5
)
2
{\displaystyle =(10+0.5)^{2}\,}
=
110.25
{\displaystyle =110.25\,}
The minimum area of the square:
{\displaystyle {\text{The minimum area of the square:}}\,}
=
(
10
−
0.5
)
2
{\displaystyle =(10-0.5)^{2}\,}
=
90.25
{\displaystyle =90.25\,}
The difference between the maximum area and the measured area:
{\displaystyle {\text{The difference between the maximum area and the measured area:}}\,}
=
110.25
−
100
{\displaystyle =110.25-100\,}
=
10.25
{\displaystyle =10.25\,}
The difference between the minimum area and the measured area:
{\displaystyle {\text{The difference between the minimum area and the measured area:}}\,}
=
100
−
90.25
{\displaystyle =100-90.25\,}
=
9.75
{\displaystyle =9.75\,}
∵
10.25
>
9.75
{\displaystyle \because 10.25>9.75\,}
∴
The accumulated error
=
10.25.
{\displaystyle \therefore {\text{The accumulated error}}=10.25.\,}
And now back to Joe Bloggs
edit
