Why are uncertainties often given in percentage form?

Uncertainties are often given in percentage form to provide a relative measure of the error compared to the size of the measurement.

Uncertainties in measurements are an inevitable part of any scientific experiment. They provide an estimate of how much the measured value could deviate from the 'true' value. When these uncertainties are expressed as a percentage, they give a relative measure of the error. This means that the uncertainty is compared to the size of the measurement itself. This is particularly useful when comparing uncertainties across different measurements or experiments, as it allows for a fair comparison regardless of the actual size of the measurements.

For example, an uncertainty of 1 cm in a measurement of 1 m (100 cm) is a relatively small error (1%), whereas the same uncertainty in a measurement of 10 cm is a much larger error (10%). By expressing uncertainties as a percentage, we can clearly see that the second measurement is less precise than the first, even though the absolute uncertainty is the same in both cases.

Furthermore, expressing uncertainties in percentage form can also help in understanding the significance of the error. If the percentage uncertainty is small, it suggests that the measurement is quite precise and the error is not likely to have a significant impact on the results or conclusions drawn from the data. On the other hand, a large percentage uncertainty indicates a less precise measurement and suggests that the error could significantly affect the results or conclusions.

In addition, percentage uncertainties are often used when calculating the propagation of uncertainties in calculations involving multiplication or division. In these cases, the percentage uncertainties are simply added together, making the calculations straightforward and easy to follow.

In conclusion, percentage uncertainties provide a relative measure of the error, allowing for easy comparison across different measurements and a clear understanding of the significance of the error. They also simplify the calculation of propagated uncertainties in certain mathematical operations.