Approximate calculations. Approximation error

In practice we often work with approximate values of quantities: when counting many objects, when measuring with instruments, when rounding numbers. A value found by counting, such as the number of pupils in a class, is exact, while a measurement is usually approximate. If x is the exact value of a quantity and a is its approximate value, the modulus of the difference |x - a| is the absolute error of the approximation (or simply the error). The smaller the error, the more accurate the approximation. We take the modulus because what matters is how far, not in which direction, the approximation is from the exact value.