Error Handling!
Some ideas….
(4.8  0.7) x 10-3
Aim – Coursework II
B8a Description of action proposed to minimise errors It is acceptable
for this to be in the plan.
B8b Implementation of plan to minimise errors Often indicated by
results  for example, timing of multiple oscillations, taking a
background count. A comment from the candidate that this has been
carried out is required.
B8c Checks inconsistent or suspect readings. A statement by candidate
that readings have been checked is required.
Main Ideas…
 Why are errors important?
 Types of error – random and systematic (precision and
accuracy)
 Estimating errors
 Quoting results and errors
 Treatment of errors in formulae
Random vs systematic errors
Random errors only
True value
Random + systematic
A result is said to be accurate if it is relatively free
from systematic error
A result is said to be precise if the random error is
small
Quoting results and errors
 Generally state error to one significant figure
(although if one or two then two significant
figures may be used).
 Quote result to same significance as error
 When using scientific notation, quote value and
error with the same exponent
Quoting results and errors
 Value 44, error 5  445
 Value 128, error 32  13030
 Value 4.8x10-3, error 7x10-4  (4.80.7)x10-3
 Value 12.345, error 0.35  12.30.4
Don’t over quote results to a level inconsistent
with the error 36.6789353720.5 
Estimating reading errors 1
Oscilloscope – related to width of trace
3.8 divisions @ 1V/division = 3.8V
Trace width is ~0.1 division = 0.1V
(3.80.1)V
Estimating reading errors 2
Digital meter – error taken as 5 in next
significant figure
(3.3600.005)V
Estimating reading errors 3
Analogue meter – error related to width of pointer
Value is 3.25V
Pointer has width 0.1V
(3.30.1)V
Estimating reading errors 4
16
17
Linear scale (e.g. a ruler)
Need to estimate precision with which measurement
can be made
May be a subjective choice
16.770.02
Estimating reading errors 5
16
17
16
17
•The reading error may be dependent on what is
being measured.
•In this case the use of greater precision equipment
may not help reduce the error.
Error manipulation +/If you add or subtract two quantities with the same units
you must add their absolute errors
i.e.
(300m  5)m + (200  15)m = (500  20)m
 The maximum reading could have been = 520m
 The minimum reading could have been = 480m
Error manipulation * or /
If you multiply or divide two quantities with different units
you must add their percentage error
v = (300m  30)m / (200  10)s
% errors are 10% for distance , 5% for time.
v = 300m / 200s = 1.5 m/s  15%
v = (1.5  0.225 )m/s
NB if you are dealing with r2 that is the same as r*r so you
can use this method with that as well.
Example of error manipulation 1
Where r = (5  0.5) m
A r
2
A = 78.5398 m2
Error in the radius is either found as an
absolute or % error
Hence 0.5 / 5 = 0.1 or 10%
Total error = 2 * 10% = 20%
Hence final result is;
A = (79  16)m2
or
A = 79m2  20%
A
r
The Complex Formulae
This theory in “real” maths talk is shown below. With the
example we did for Area!
 Z 
Z  ABC
2
  A    B    C 
2
2
2
2
n
m
2
 Z 
 A 
 B 
 C 

 
 
 

Z
A
B
C








Z  A B C or A B / C etc
Z  A B C
2
2
2
2
 Z 
 A 
 B 
 C 

  n
 m
  l

Z
A
B
C








l
2
2
A

r
0.5
Z  ln A  0.1 Z 
A
r
5
Z
 A  r 
Z Aexp
(2A0.1) 2  0.04

2





 A 
 r Z
2

A
A
2
 0.2
hence
 A  0.2  A
 A  0.2  (78.5398 m )  16 m
2
2