How does one calculate the total uncertainty of multiple measurements?

To calculate the total uncertainty of multiple measurements, add the individual uncertainties in quadrature.

When taking multiple measurements, each measurement will have its own uncertainty. To calculate the total uncertainty, these individual uncertainties must be combined. This is done by adding them in quadrature.

Adding in quadrature means that the uncertainties are added as squares, and then the square root is taken of the sum. For example, if one measurement has an uncertainty of 0.5 and another has an uncertainty of 0.3, the total uncertainty would be:

√(0.5² + 0.3²) = √(0.25 + 0.09) = √0.34 = 0.58

This means that the total uncertainty of the measurements is 0.58. It is important to note that uncertainties should always be expressed to one significant figure, so the final answer would be 0.6.

It is also important to consider the units of the measurements when calculating the total uncertainty. If the measurements have different units, they must be converted to the same units before adding in quadrature.

Overall, adding uncertainties in quadrature is a useful method for calculating the total uncertainty of multiple measurements, and is an important skill for A-Level Physics students to master.