Loss of Significance - Demonstration of The Problem

Demonstration of The Problem

The effect can be demonstrated with decimal numbers. The following example demonstrates loss of significance for a decimal floating-point data type with 10 significant digits:

Consider the decimal number

A floating-point representation of this number on a machine that keeps 10 floating-point digits would be

which is fairly close – the difference is very small in comparison with either of the two numbers.

Now perform the calculation

The answer, accurate to 10 digits, is

However, on the 10-digit floating-point machine, the calculation yields

Whereas the original numbers are accurate in all of the first (most significant) 10 digits, their floating-point difference is only accurate in its first nonzero digit. This amounts to loss of significance.