p-Adic Numbers

From the start, most students are introduced to rational and irrational numbers. We are taught how to construct these numbers by setting axioms and properties. We also learn about prime numbers and the properties associated with it. But at the end before most students graduate, they may not even know that there exists a whole set of different type of numbers known as the p-adic numbers.

The p-acid numbers builds upon the arithmetic of the rational numbers. As for the arithmetic of p-acid numbers, where $p$ is a prime, the process is different than what we have been used to seeing. The difference comes from the alternative definition of absolute values on $Q$.

An interesting question asked is:

Find the $7$-acid expansion of $-1$.