Is Floating-Point Multiplication Accurate in .NET?

Floating-Point Arithmetic in .NET: Understanding Inaccuracies

A common question regarding .NET's floating-point arithmetic is whether it's inherently flawed. This doubt often arises from unexpected results like the following:

<code>double i = 10 * 0.69;</code>

This simple multiplication yields 6.8999999999999995, a result that deviates from the expected 6.9. This discrepancy isn't a flaw in .NET itself, but rather a consequence of how floating-point numbers are represented and processed.

Floating-point numbers are stored as approximations in binary format. While integers can be represented exactly, many decimal numbers (like 0.69) don't have an exact binary equivalent. This inherent limitation leads to small rounding errors during calculations. The situation is analogous to the inability to precisely represent 1/3 as a finite decimal (0.333...).

The seemingly minor inaccuracy in the example above highlights the limitations of floating-point representation. For a deeper understanding of the underlying principles, further exploration of binary floating-point representation and its inherent limitations is recommended.

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