How to calculate the uncertainty when quantities are multiplied or divided?

To calculate the uncertainty when quantities are multiplied or divided, use the percentage uncertainties.

When multiplying or dividing quantities, the percentage uncertainties are added together to find the overall percentage uncertainty. For example, if the percentage uncertainty for one quantity is 2% and for another quantity is 3%, then the overall percentage uncertainty when multiplying or dividing them is 5%.

To find the absolute uncertainty, multiply the overall percentage uncertainty by the value of the quantity. For example, if the overall percentage uncertainty is 5% and the value of the quantity is 10, then the absolute uncertainty is 0.5.

When dividing a quantity by a constant, the percentage uncertainty of the quantity remains the same, but the absolute uncertainty changes. To find the new absolute uncertainty, divide the original absolute uncertainty by the value of the constant.

It is important to note that when adding or subtracting quantities, the absolute uncertainties are added together to find the overall absolute uncertainty, rather than the percentage uncertainties. This is because the uncertainty in the sum or difference is not affected by the scale of the quantities, unlike when multiplying or dividing.

Understanding the differences between precision and accuracy can also enhance your approach to calculating uncertainties, as these concepts are fundamental in measurements.

Moreover, recognising the impact of random errors on your measurements is crucial for correctly estimating uncertainty in experimental outcomes.

For further detail on error analysis, exploring the differences between systematic and random errors provides additional insights that are beneficial for advanced physics students.

A-Level Physics Tutor Summary: When you multiply or divide numbers, add their percentage uncertainties together to get the total percentage uncertainty. Then, to find the absolute uncertainty, multiply this percentage by the main quantity's value. If dividing by a constant, the percentage uncertainty stays the same, but absolute uncertainty changes. Remember, for addition or subtraction, you add the absolute uncertainties instead.