The set of rational numbers, denoted by $\m Q$ is the set $\{\frac{m}{n}\ |\ m,n\in \m Z \text{and} n\ne 0\}$ $=$ the set of all numbers with finite or (eventually) repeating decimal expansions.
The set of real numbers, denoted by $\m R$ is the set $(-\infty,\infty)=$ the real line $=$ the set of all numbers with finite or infinite decimal expansions.
The set of irrational numbers is the set $\{x\in \m R\ |\ x\notin \m Q\}$ $=$ the set of all numbers with non-repeating decimal expansions.