1. The problem is to determine whether a given number is rational or irrational. 2. A rational number is any number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. 3. An irrational number cannot be expressed as a simple fraction; its decimal form is non-terminating and non-repeating. 4. Examples: $\frac{1}{2}$ is rational because it is a fraction of integers. 5. $\sqrt{2}$ is irrational because it cannot be expressed as a fraction and its decimal goes on without repeating. 6. To classify a number, try to express it as a fraction or check its decimal expansion. 7. If it can be expressed as a fraction, it is rational; otherwise, it is irrational.