Floating point numbers are demystified in Bartosz Ciechanowski’s detailed exploration of IEEE 754 standards. His companion tool, float.exposed, visualizes how decimal values like 0.2 become distorted in binary systems, revealing why 0.200000003 appears instead of exact precision. The article breaks down binary scientific notation, showing how 327.849 converts to 1.01000011×2⁸, and explains rounding errors when limited significand bits truncate infinite binary fractions. IEEE 754’s bias value of 127 ensures exponents stay non-negative, while the implicit leading ‘1’ in significands saves storage space.

These technical nuances matter because 2³⁰⁰ or 2⁻³⁰⁰ can’t fit within float’s [−126, +127] exponent range, causing overflow/underflow errors.