We are going to cover measurement and different types of uncertainty.
There are some rules that you need to know regarding Measurement and Uncertainty
- no measurement is exact
- every measurement is a best estimate which has some degree of uncertainty
- only when we count a set of objects, we get an exact number
This is expressed in units of measurement; not ratio
In order to express uncertainty:
- Make at least 3 measurements
- Calculate average
- Absolute uncertainty is the largest difference between the average and lowest or highest reasonable measurement
- Discard unreasonable data
Calculate the average of these numbers ((47+48+45+46)/4)) = 46.5
Then calculate the difference 46.5- 45 = 1.5 or 48 - 46.5 = 1.5 (does not matter because the result is the same)
Therefore + 1.50cm is the absolute uncertainty.
Absolute uncertainty:
This is determined by uncertainty of each instrument
- Always measure to the best precision
- Estimate to 1/10 or 0.1 of the smallest segment of the instrument scale
Take a ruler
The smallest scale is 0.1cm
0.1 of the scale is 0.01 cm
Therefore the absolute uncertainty is 0.01cm
This is how you express it: (the average value) + (absolute uncertainty)
Eg. 15.6 + 0.03cm
Don't forget the units.
Relative Uncertainty
Relative Uncertainty is absolute uncertainty/estimated measurement
It is expressed in percent or significant figures(the number of significant figures indicates relative uncertainty; the last digit is uncertain)
Written by JK (Oct 31,2010)