explain how to distinguish between a rational number and an irrational number.

Brief Explanations:

A rational number can be expressed as a fraction $\frac{p}{q}$ where $p,q$ are integers and $q\neq0$. Its decimal - expansion is either terminating (e.g., $0.5=\frac{1}{2}$) or repeating (e.g., $0.\overline{3}=\frac{1}{3}$). An irrational number cannot be written as a fraction of two integers and has a non - terminating, non - repeating decimal expansion, like $\pi = 3.1415926535\cdots$ and $\sqrt{2}=1.41421356237\cdots$.

Answer:

A rational number can be written as a fraction $\frac{p}{q}$ ($p,q\in\mathbb{Z},q\neq0$) with a terminating or repeating decimal expansion. An irrational number cannot be written as a fraction and has a non - terminating, non - repeating decimal expansion.