Error Handling!

Some ideas….

(4.8 0.7) x 10-3

Aim – Coursework IIB8a 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

True value

Random errors only

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

Value 44, error 5 445

Value 128, error 32 13030

Value 4.8x10-3, error 7x10-4 (4.80.7)x10-3

Value 12.345, error 0.35 12.30.4

Don’t over quote results to a level inconsistent with the error 36.6789353720.5

Quoting results and errors

Estimating reading errors 1

Oscilloscope – related to width of trace3.8 divisions @ 1V/division = 3.8VTrace width is ~0.1 division = 0.1V(3.80.1)V

Digital meter – error taken as 5 in next significant figure

(3.3600.005)V

Estimating reading errors 2

Analogue meter – error related to width of pointerValue is 3.25V

Pointer has width 0.1V

(3.30.1)V

Estimating reading errors 3

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 choice16.770.02

Estimating reading errors 5

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.

16 17

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 12A rWhere r = (5 0.5) m

A = 78.5398 m2

Hence final result is;

A = (79 16)m2 or A = 79m2 20%

Ar

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%

The Complex FormulaeThis theory in “real” maths talk is shown below. With the example we did for Area!

2 22

2 2

0.50.1

5

2 (2 0.1) 0.04

0.2 0.2 0.2 (78.5398 ) 16

r

r

A r

A r

Ahence A A A m m

A