When 0.1 + 0.2 ≠ 0.3: The IEEE 754 Standard That Broke Your Calculations
Type 0.1 + 0.2 into any browser console, Python REPL, or JavaScript runtime. The answer comes back as 0.30000000000000004. This isn’t a bug. It’s not an error in your programming language. It’s the inevitable consequence of a fundamental tension: humans count in base 10, but computers count in base 2. The IEEE 754 floating-point standard, adopted in 1985, unified how computers represent decimal numbers. Before this standard, different machines handled floating-point arithmetic differently—code that worked on one system could produce completely different results on another. William Kahan, the primary architect of IEEE 754, designed a system that traded perfect precision for predictability. Every programmer would get the same answer, even if that answer wasn’t mathematically exact. ...