The system of real numbers are defined mathematically as a 'completion' of the rational numbers. But this is not the only way to do it! In fact there are infinitely many others completions- the so called 'p-adic numbers'. These numbers were defined for pure mathematical reasons and have been a subject of research for a century. But in the last 3 decades they have found 'real world' applications in computer science, construction of networks, algorithms etc. We will try to tell the story in a way which hopefully will make sense also to non-mathematicians.