How do you calculate the percentage uncertainty?

You calculate the percentage uncertainty by dividing the absolute uncertainty by the measured value and then multiplying by 100%.

In more detail, the percentage uncertainty is a way of expressing the uncertainty of a measurement as a percentage of the measured value. It is a useful tool in physics because it allows you to compare the uncertainties of different measurements, even if those measurements are of different quantities or are expressed in different units.

To calculate the percentage uncertainty, you first need to know the absolute uncertainty of your measurement. The absolute uncertainty is a measure of the range within which the true value of the measurement is likely to lie. It is usually given as a ± value. For example, if you measure the length of a piece of string to be 20 cm ± 1 cm, the absolute uncertainty is 1 cm.

Next, you divide the absolute uncertainty by the measured value. In the example above, you would divide 1 cm by 20 cm to get 0.05. This gives you the fractional uncertainty.

Finally, to convert the fractional uncertainty to a percentage, you multiply by 100%. So, 0.05 becomes 5%. This means that the length of the string is 20 cm ± 5%.

It's important to remember that the percentage uncertainty is not a measure of the accuracy of the measurement. It is a measure of the precision of the measurement, or how well the measurement is defined. A small percentage uncertainty means that the measurement is well defined, while a large percentage uncertainty means that the measurement is poorly defined.

In physics, it's often more useful to work with percentage uncertainties than with absolute uncertainties. This is because percentage uncertainties allow you to compare the uncertainties of different measurements on an equal footing. For example, if you're comparing the uncertainties of measurements of length and time, it wouldn't make sense to compare the absolute uncertainties because they're expressed in different units (cm and s). But you can compare the percentage uncertainties because they're unitless. To further understand the concepts of measurement in physics, exploring topics like precision vs accuracy, random errors, systematic errors, and absolute vs relative uncertainty can provide deeper insights into the significance of precision and accuracy in scientific measurements.

IB Physics Tutor Summary: To calculate percentage uncertainty, divide the absolute uncertainty (the ± value) by the measurement, then multiply by 100. This tells you how uncertain a measurement is as a percentage of its value. It helps compare different measurements accurately, regardless of their units. Remember, it reflects the precision of the measurement, not how correct it is.