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

0.1234567891234567890

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

0.1234567891

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

Now perform the calculation

0.1234567891234567890 − 0.1234567890

The answer, accurate to 10 digits, is

0.0000000001234567890

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

0.1234567891 − 0.1234567890 = 0.0000000001

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.

Read more about this topic:  Loss Of Significance

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