Tiny changes in a starting point can cause wildly different results — and precision itself counts as a starting condition. When you run the iterative equation x(n+1) = rx(n)(1-x(n)) at different rounding levels, something striking happens: just changing the decimal precision, without touching the math itself, can switch the outcome from alternating to steady. Across 26 rounds with constants r ranging from 2.70 to 3.70, some values settle on one number, others alternate between two, and still others spiral into total unpredictability. That shift from order to chaos driven by rounding alone — not by any change in the equation — is chaos theory made visible in a spreadsheet.