Undergrad Why Does Subtractive Cancellation Affect Measurement Precision?

[Roger Dodger]

When subtracting measurements that each have a certain level of uncertainty, we can end up with huge levels of error if the two measurements are roughly equal in value. However, this problem doesn't appear when adding numbers.

Question: Is there a name for this type of error? Does anyone discuss the problems associated with subtracting measurements that are similar in magnitude? I can't seem to find anything on this source of error, possibly because I don't know what it's called.

In numerical analysis, they call this subtractive cancellation or significance loss and the uncertainty in the numbers is due to the truncation of numbers to fit in a computer's memory. But I cannot find anything on this effect for experimental measurements.

 

[Dale]

It is usually called the propagation of errors or propagation of uncertainty. The uncertainty is not larger from subtracting rather than adding. The difference is the size of the estimate. This makes the relative uncertainty larger because the relative uncertainty is the uncertainty divided by the estimate.