Why does Python tell you that 0.1 + 0.2 = 0.30000000000000004? The answer is IEEE 754 - the floating-point standard baked into every CPU on the planet. In this video we go under the hood: from the limits of fixed-point arithmetic, through scientific notation in binary, to hand-converting 3.14 into its 32-bit IEEE 754 representation - and then proving it in C with a union hack that reads the raw bits directly out of memory. We also look at what happens at the edges: divide by zero, and rather than a crash you get infinity. Divide zero by zero and you get NaN - Not a Number. IEEE 754 doesn't just define the happy path, it defines all the weird paths too. ━━━━━━━━━━━━━━━━━━━━━━━━ CHAPTERS ━━━━━━━━━━━━━━━━━━━━━━━━ 0:00 The 0.1 + 0.2 Problem 1:01 Fixed-Point Arithmetic 5:57 Scientific Notation & the Birth of Floating Point 6:48 The IEEE 754 Standard 7:01 Converting 3.14 to a 32-bit Float 11:12 Proving it in C 13:24 Edge Cases: Infinity and NaN 15:20 Why IEEE 754 Changed Everything ━━━━━━━━━━━━━━━━━━━━━━━━ LINKS & RESOURCES ━━━━━━━━━━━━━━━━━━━━━━━━ Support the channel on Patreon (+ 24hr early access, no ads): https://www.patreon.com/ncot_tech Scientific Calculator - Thirunavukkarasye-Raveendran, CC BY 4.0 https://creativecommons.org/licenses/by/4.0, via Wikimedia Commons Intel 486 DX2 Die shot - This file was derived from: Intel 80486 DX2 die.JPG by Pauli Rautakorpi CC BY 3.0 Music by Karl Casey @ White Bat Audio