The approximation error in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because
#the measurement of the data is not precise due to the instruments. (e.g., the accurate reading of a piece of paper is 4.5 cm but since the ruler does not use decimals, you round it to 5 cm.) or
#approximations are used instead of the real data (e.g., 3.14 instead of pi|π).
In the mathematics|mathematical field of numerical analysis, the numerical stability of an algorithm in numerical analysis indicates how the error is propagated by the algorithm.