Computers and Mathematics

Numerical Analysis · Axiom Academy

INTRO Computers and Mathematics Discover why computers can't represent all numbers—and what that means for computation. What is 1 divided by 3? Click to see what a computer actually stores: Computers use binary (0s and 1s). Watch how the number changes as we adjust the bits: Click the bits to toggle them! Let's test: does 0.1 + 0.2 equal 0.3? Make your prediction, then compute: Small errors might seem harmless, but watch what happens when we repeat an operation many times: Computers have limited memory and can only represent a finite set of numbers. Most real numbers must be approximated. Every floating-point operation may introduce small errors. The key is understanding and controlling these errors, not eliminating them. Numerical analysis teaches us to write algorithms that produce results accurate enough for our needs, despite these limitations.

This is the written version of the interactive lesson above. See the full Numerical Analysis course.