Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.
I measure a rectangle with my ruler, and find L = 10 +/- 1 cm and w = 5 +/- 1 cm.
How good is each measurement? We can use the fractional uncertainty, or percent uncertainty, to quantify the precision of a measurement.
To compute the area of the rectangle, I multiply length times width:
The rules for propagation of error state that when two quantities are multiplied, their fractional uncertainties are added:
And now, since I know the value of the area and its fractional uncertainty, I can compute the uncertainty in the area.
Finally, I can write the area of the rectangle together with its uncertainty:
Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.