HallsofIvy said:Use the "differential"- R = (h2+l2)/2h [itex]dR= [(1- 2(h^2+ l^2))/h^2]dh+ (l/h)dl. Set dh and dl equal to the uncertainties in h and l respectively. You will need "current" values for h and l as well as for dh and dl. I do not understand you last values. Where you have "h = ±0.57%" do you mean the uncertainty in h (my "dh") rather than h itself? Also you have "h2=±1.14%" which is 2 times your h, not h squared.
You are confusing me by saying "actual uncertainty" at one point and "% uncertainty" at another- those are NOT the same thing. If h= 10, say, and the "actual uncertainty" (I would say "relative error") is 0.5 then the "percentage uncertainty" is (0.5)/(10)= 0.05= 5%. If f(x)= x2 then df= 2x(dx) The "actual uncertainty in f is 2 times the value of f time the "actual uncertainty" in x. The "percent uncertainty" in f is df/f. Dividing both sides of the previous equation by f, df/f= 2x(dx)/f= 2x(dx)/x2= 2(dx/x) so the percent uncertainty in x2 is 2 times the percent uncertainty in x.Ch3m_ said:Yeah those are the actual uncertainties in the values
h = ±0.57% is the % uncertainty, where h is a measurement of length in m
To get the uncertainty in h2 you multiply the %uncertainty of h by 2 yeah?
Overall uncertainty is a measure of the total amount of uncertainty in a scientific measurement or calculation. It takes into account all sources of error and variability and provides a single value to represent the level of uncertainty in the final result.
Overall uncertainty is typically calculated by combining the individual uncertainties from each source of error using mathematical operations such as addition, subtraction, multiplication, and division. This process is known as error propagation.
Considering overall uncertainty is important because it allows scientists to understand the level of confidence they can have in their results. It also allows for accurate comparisons between different measurements or calculations, as the overall uncertainty provides a standard measure for the level of uncertainty in each result.
Some common sources of uncertainty include human error, instrument error, environmental factors, and limitations of measurement techniques. Other sources of uncertainty may vary depending on the specific scientific experiment or calculation being performed.
Overall uncertainty can be reduced by minimizing the sources of error and variability in a measurement or calculation. This can be achieved through careful experimental design, proper use and calibration of instruments, and repetition of measurements to account for random errors. Additionally, using more precise measurement techniques and increasing the sample size can also help reduce overall uncertainty.