An irrational number is one that has no defined ending. EVER. Meaning that as far as we calculate, there will always be infinite more numbers extending away. A rational number is one that has a defined ending, or at least one that we can see. There are two main types: a repeating decimal, or a terminating decimal. An example of a repeating decimal would be 2/3, or 0.6666666 repeating. This number goes on forever, but we know what each number is, so that's okay. An example of a terminating decimal is one that just...ends, such as 1/2, which in decimal form is just 0.5.