Irrational numbers are numbers that are not rational. That would mean that irrational numbers cannot be represented as a fraction or ratio of two integers. That is, irrational numbers cannot be shown in the form $\frac{a}{b}$.

A famous example of an irrational number is $\pi$ (pi). is a number that is obtained when you take the ratio of a circle’s circumference to its diameter.

The decimals go on forever without repeating. So there is no way to representas a ratio of two integers.

There are approximations of $\pi$ that can be represented as a ratio of two integers, the most common is $\frac{22}{7} = 3.142857143$ another is $\frac{355}{113} = 3.14159292$

Indeed the 2nd approximation shows a value that is much more close to $\pi$.

Other examples of irrational numbers includeewhich is another number like $\pi$. $\sqrt{2}$ is also another example of an irrational number. In fact, the square roots of any positive integer ($ℤ_+$) is always irrational except when the integer is a perfect square. If you do not know what a perfect square is, do not worry you will come across it soon. Examples of perfect sqaures include $4, 9, 16$ and so on.