To calculate the percentage uncertainty of a measurement, you divide the absolute uncertainty by the measured value and then multiply the result by $100\%$.

In more detail, percentage uncertainty expresses the uncertainty of a measurement as a percentage of the measured value. This is particularly useful in physics, as it allows for the comparison of uncertainties across different measurements, even when those measurements involve different quantities or units.

To begin, you need to determine the absolute uncertainty of your measurement. The absolute uncertainty represents the range within which the true value of the measurement is expected to lie and is typically denoted by a ± value. For instance, if you measure the length of a piece of string to be $20 \, \text{cm} \pm 1 \, \text{cm}$, the absolute uncertainty in this case is $1 \, \text{cm}$.

Next, you divide the absolute uncertainty by the measured value. Using the previous example, you would calculate:

To convert the fractional uncertainty into a percentage, you multiply by $100\%$. Therefore, $0.05$ becomes $5\%$. This indicates that the length of the string can be expressed as $20 \, \text{cm} \pm 5\%$.

It is crucial to note that percentage uncertainty does not measure the accuracy of a measurement; rather, it reflects the precision of the measurement—essentially how well-defined the measurement is. A small percentage uncertainty indicates that the measurement is precise, while a large percentage uncertainty suggests that it is less well-defined.

In physics, working with percentage uncertainties is often more advantageous than using absolute uncertainties. This is because percentage uncertainties provide a common ground for comparing different measurements irrespective of their units. For example, when comparing uncertainties in measurements of length (in cm) and time (in s), comparing absolute uncertainties directly would be impractical due to differing units. In contrast, percentage uncertainties are unitless and can be compared directly.

To deepen your understanding of measurements in physics, consider exploring topics such as precision, accuracy, significant figures, and error analysis. These concepts will enhance your grasp of the importance of precision and accuracy in scientific measurements.

Summary for IB Physics Tutoring: To calculate the percentage uncertainty, divide the absolute uncertainty (the ± value) by the measured value, then multiply by $100$. This process quantifies the uncertainty of a measurement as a percentage of its value, facilitating accurate comparisons between different measurements regardless of their units. Remember, it reflects the precision of the measurement, not its accuracy.