How do irrational numbers differ from rational numbers?

For certain integers p and q (where ${\displaystyle q\ne 0}$), rational numbers can be represented in the manner ${\displaystyle \frac{p}{q}}$. Since ${\displaystyle n=\frac{n}{1}}$ for every integer, it should be noted that this covers numbers. A few examples of rational numbers include 5, ${\displaystyle \frac{1}{2}}$, ${\displaystyle \frac{17}{3}}$, and ${\displaystyle -\frac{7}{2}}$. An irrational number is any other Real number. ${\displaystyle \sqrt{2}}$, ${\displaystyle \pi }$, and e are a few examples of irrational numbers. If x is a rational number, then the decimal expansion of x will either end or repeat.
As an illustration, ${\displaystyle \frac{213}{7}=30.428571428571...}$, which we might represent as 30. (428157).
The decimal expansion of an irrational number will neither terminate nor recur. For instance, ${\displaystyle \pi }$ = 3.141592653589793238462643383279502884...