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
0.1234567891234567890A floating-point representation of this number on a machine that keeps 10 floating-point digits would be
0.1234567891which is fairly close – the difference is very small in comparison with either of the two numbers.
Now perform the calculation
0.1234567891234567890 − 0.1234567890The answer, accurate to 10 digits, is
0.0000000001234567890However, on the 10-digit floating-point machine, the calculation yields
0.1234567891 − 0.1234567890 = 0.0000000001Whereas 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.
Read more about this topic: Loss Of Significance
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