Why 0.1+0.2 != 0.3, or the Mysterious World of Floating-Point Numbers
summary
Explains why decimal sums like 0.1+0.2 do not equal 0.3 due to floating-point representation and arithmetic. Covers how computers represent real numbers in binary (IEEE 754), the resulting rounding errors and pitfalls in PHP and similar languages, and practical implications for developers.
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chapters (20)
- 0:00Introduction
- 1:251+0.2 != 0.3 problem
- 4:18Floating-point precision
- 6:24Binary representation
- 12:25Floats vs integers
- 14:13Floating limits
- 17:45Unexpected precision loss
- 18:47IEEE 754 standard
- 19:30Ariane 5 failure
- 24:08Patriot missile failure
- 30:533D calculations
- 32:38PHP floats experiment
- 33:20Database storage
- 35:05Data transmission
- 36:05Scientific use cases
- 37:49Money problems
- 39:34Solutions for money
- 40:38Alternatives to floats
- 41:42Java BigDecimal
- 42:02Conclusion
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