An integer number is a number that can be written without using a rational component. In other words, if a number can be written without using a fraction, then that number is considered an integer.
For example, let's take the first number:
This number is written as a fraction. But, this is also equivalent to:
Since it can also be written without making use of a fraction then this number is an integer.
Also, there are numbers that are written in decimal form. For example:
These types of numbers are not integers.