3.2. Unit Conversions, Error, and Uncertainty http://www.ck12.org
Percent Uncertainty
To express the uncertainty in a measurement, we can calculatepercent uncertainty. Percent uncertainty is the ratio
of the uncertainty to the measured value, multiplied by one-hundred. For instance, the percent uncertainty associated
with the measurement of (52.9±0.5 mL), would be
% uncertainty=
0. 5
52. 9
× 100 = 0 .95%≈1%
Example 3.10
Using our estimate of 52.9 mL, what would be the range of possible values for the true volume?
Answer
Upper estimate = 52.9 + 0.5 = 53.4 mL
Lower estimate = 52.9 - 0.5 = 52.4 mL
Assuming that our equipment is accurate, we can be confident that the true volume of the sample is somewhere in
between these two values.’
Percent Error
On the other hand,percent erroris an expression of the accuracy of a measurement. There are various possible
sources of error that arise in measurement. For example, there can be error associated with the observation, like
misreading a graduated cylinder. There is error associated with the method or the procedure, like not drying a wet
solid before weighing. Error can also arise from the object being measured. For example, a pure solid may have a
residue fixed to it that affects its mass. There can also be errors that arise from the measurement instrument, like not
zeroing a balance, or improper calibration. Percent error is calculated as follows:
% error=
|Measured−Accepted|
Accepted
× 100
Example 3.11
Make an estimate of volume for the image shown inFigure3.6, and answer the questions below.
FIGURE 3.6
Which of the following estimates would be accurate? Report your answer in terms of uncertainty.