## Uncertainty and percentage errors

Experimental data is never exact. There is always an element of uncertainty in the data due to:

- the precision of the equipment;
- imperfections in the experimental procedure; and
- judgements made by the operators.

Experimental uncertainties are those which cannot be quantified and often arise from making a judgement. For example, judging the end point of a titration by a colour change.

Quantitative uncertainty is usually expressed as a percentage error. This value is calculated from the accuracy of the apparatus and by taking readings from the scientifc apparatus.

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Percentage errors can be calculated using the expression:

% error = [(difference between measurement value and accepted value)/accepted value] x 100

The lower the percentage error, the more accurate the piece of equipment is. The overall percentage error for an experiment is the sum of the individual percentage errors for each peice of equipment.

If 20 cm^{3} of copper sulfate solution was measured out using the measuring cylinder in the image above, what would the % error be?

(0.5 (cm^{3}) / 20.0 (cm^{3}) ) x 100 = 2.5%

Suggest how you might reduce this % error.

Use a 25 cm^{3 }measuring cylinder with a larger scale that is accurate to +/– 0.1 cm^{3}.

Accuracy in volume measurement is a practical activity in which students explore and compare the accuracy of a burette, a graduated measuring cylinder and a beaker. Please note that with in this activity the unit of volume used is mL rather than cm^{3}.