The floating point: Tales of the unexpected

Digital computation is central to almost all scientific endeavors and has become integral university physics education. Students collect experimental data using digital devices, process spreadsheets graphical software, develop programming skills for modeling, simulation, computational work. Issues associated with the floating-point representation of numbers are rarely explored. In this article, problems floating point divided into three categories: significant-figure limits, propagation error, rounding. For each category, examples presented unexpected ways, in which can impact veracity results. These cover aspects classical dynamics, numerical integration, cellular automata, statistical analysis, timing. Suggestions made curriculum enhancement project-style investigations that reinforce issues covered at a level suitable undergraduate students.