p-adic expansions are a way to represent numbers using a base that is a prime number, denoted as p. In this system, numbers are expressed in terms of powers of p, allowing for a unique representation of integers and rational numbers. The digits in a p-adic expansion can be thought of as coefficients for these powers, extending infinitely in the negative direction. This concept is part of p-adic number theory, which studies the properties of numbers in relation to a prime p. Unlike traditional decimal or binary systems, p-adic expansions focus on divisibility and congruences, providing insights into number theory and algebraic structures.