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.