Absolute error represents the actual difference between a measured value and the true value, whereas relative error expresses this difference as a percentage of the true value.

To elaborate, absolute error quantifies how far a measurement deviates from the true or accepted value. It is calculated by determining the absolute difference between the measured value and the true value. For instance, if you measure the length of a table to be $1.02$ metres, but the actual length is $1.00$ metre, the absolute error would be:

This provides a clear and straightforward indication of the measurement error.

In contrast, relative error assesses the absolute error in relation to the magnitude of the quantity being measured. It is calculated by dividing the absolute error by the true value and then multiplying by $100$ to convert it into a percentage. Using the table example, the relative error can be calculated as follows:

This percentage provides insight into the significance of the error relative to the size of the measurement. A $2\%$ error might be acceptable when measuring a table, but it would be far less tolerable when measuring the concentration of a chemical in a solution for a chemistry experiment.

Both absolute and relative errors hold significance in different contexts. Absolute error offers a direct measure of the deviation from the true value, which can be essential when knowing the exact extent of the measurement error is crucial. However, it does not convey the significance of this error in relation to the size of the measurement. This is where relative error becomes valuable. By expressing the error as a percentage of the true value, it helps in understanding the relative impact of the error. This distinction is particularly important in fields like chemistry, where a small absolute error may represent a large relative error, potentially influencing the outcome of an experiment.