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 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  44  5  Value 128, error 32  130  30  Value 4.8x10 -3, error 7x10 -4  (4.8  0.7)x10 -3  Value , error 0.35  12.3  0.4 Don’t over quote results to a level inconsistent with the error  0.5 Quoting results and errors 

Estimating reading errors 1 Oscilloscope – related to width of trace 3.8 1V/division = 3.8V Trace width is ~0.1 division = 0.1V (3.8  0.1)V

Digital meter – error taken as  5 in next significant figure (3.360  0.005)V Estimating reading errors 2

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 3

Estimating reading errors Linear scale (e.g. a ruler) Need to estimate precision with which measurement can be made May be a subjective choice  0.02

Estimating reading errors 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. 1617

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  )m/s NB if you are dealing with r 2 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 = m 2 Hence final result is; A = (79  16)m 2 or A = 79m 2  20% A r 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 Formulae This theory in “real” maths talk is shown below. With the example we did for Area!