SI Units Quantity SI unit Symbol Mass kilogram kg Length meter m Time seconds sElectric Current ampere A Amount of mole mol substance Temperature kelvin K
Fundamental and Derived Units Quantity Symbol Base units Volume m3 mxmxm Speed ms−1 m/s Force N kg x m/s2 Pressure Pa kg x m/s2 / m2Converting Units:• Speed of Light = 300000000 ms−1 = 3.0 x 108 ms−1• Wavelength of blue light = 4.5 x 10−7 m = 0.00000045 m or 450 nm
Precision x Accuracy• Accuracy: how close a measurement is to the ‘true’ value. Example:True value: 9.87Measurements: 9.86, 9.85, 9.89, 9.88, 9.87. 9.85, 9.86• Precision: how close a measurement is to other measurementsTrue value: 9.87Measurements: 6.86, 6.85, 6.89, 6.88, 6.87. 6.85, 6.86An experiment may have great precision but be inaccurate
Look at the numbers again… Accuracy: how close a measurement is to the ‘true’ value. Example: True value: 9.87 Measurements: 9.86, 9.85, 9.89, 9.88, 9.87. 9.85, 9.86 Precision: how close a measurement is to the other measurements True value: 9.87 Measurements: 6.86, 6.85, 6.89, 6.88, 6.87. 6.85, 6.86• What could be causing the variation observed in the measurements above?• Which error can be easily reduced by simply repeating the measurement: the one associated with precision or the one associated with accuracy?
Determining % error• Remember the 2 sets of data from the previous slide. Set 1: 9.86, 9.85, 9.89, 9.88, 9.87. 9.85, 9.86 Set 2: 6.86, 6.85, 6.89, 6.88, 6.87. 6.85, 6.86• Knowing the true value is 9.87, find the % error of each set• Step 1: find the mean of each set – Set 1: 9.87 – Set 2: 6.87• Divide the mean by the true value and multiply by 100: – Set 1: 9.87/9.87 * 100 = 0% – Set 2: 6.87/9.87 * 100 = 69.6%
Random x Systematic errors• Random errors (affect precision) A random error, is an error which affects a reading at random. Sources of random errors include: – The observer being less than perfect – The readability of the equipment – External effects on the observed item• Systematic errors (affect accuracy) A systematic error, is an error which occurs at each reading. Sources of systematic errors include: – The observer being less than perfect in the same way every time – An instrument with a zero offset error – An instrument that is improperly calibrated
UncertaintyAbsolute Uncertainty• Room temperature = 22.5ºC ± 0.5Percent Uncertainty• Room temperature = 22.5ºC ± 2.2%
Determining the Uncertainty in Results• For addition and subtraction, absolute uncertainties may be added.• For multiplication, division and powers, percentage uncertainties may be added.
Error Bars• Where relevant, uncertainties should be identified as error bars in plotted quantities. Error bars may also reflect: -Range of results -Standard deviation -etc… Figure legend must be clear about what error bar means. How might the error bars influence your interpretation of the results displayed on a graph?
Significant Figures• The number of significant figures should reflect the precision of the value of the input data. e.g. 11.21 x 1.13 = 13.7883 => 13.8• Least precise: 1.13 = 3 sig fig e.g. 11.21 x 1.13 = 13.7883 => 13.8