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

When performing multiplication or division, the overall percentage uncertainty is determined by adding the individual percentage uncertainties together. For instance, if one quantity has a percentage uncertainty of $2\%$ and another has a percentage uncertainty of $3\%$, the combined percentage uncertainty for the multiplication or division of these quantities is:

To find the absolute uncertainty, you 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 $10$, the absolute uncertainty is calculated as follows:

When dividing a quantity by a constant, the percentage uncertainty of the original quantity remains unchanged, but the absolute uncertainty will be modified. To find the new absolute uncertainty, divide the original absolute uncertainty by the value of the constant.

It’s important to note that when adding or subtracting quantities, the overall absolute uncertainty is obtained by adding the absolute uncertainties of each quantity together, rather than their percentage uncertainties. This distinction arises because the uncertainty in a sum or difference is independent of the scale of the quantities involved, in contrast to multiplication or division.