What is the difference between absolute and relative error?

Absolute error is the difference between the measured value and the true value, while relative error is the absolute error divided by the true value.

Absolute error is a measure of how far a measurement is from the true value. It is calculated by subtracting the true value from the measured value. For example, if a student measures the length of a table to be 1.5 metres, but the true length is 1.6 metres, the absolute error is 0.1 metres.

Relative error, on the other hand, takes into account the size of the true value. It is calculated by dividing the absolute error by the true value. For example, if the true length of the table is 1.6 metres, the relative error is 0.1/1.6 = 0.0625 or 6.25%.

Relative error is useful when comparing the accuracy of measurements of different magnitudes. For example, if two students measure the length of the same table, but one uses a ruler with a smaller scale than the other, their absolute errors will be different, but their relative errors will be comparable.

In summary, absolute error is a measure of how far a measurement is from the true value, while relative error is a measure of how large the error is compared to the true value.