What is the difference between real and rational numbers?

The rational numbers are a subset of the real numbers. You might recall that rational numbers are those that can be expressed as the ratio of two whole numbers (no matter how large they are). Irrational Numbers, like pi, cannot. But both sets (the rational and irrational numbers) are subsets of the real numbers. In fact, when we look at all the numbers, we are looking at the complex number system. We break that down into the real and the imaginary numbers. And the real numbers have the rational and irrational numbers as subsets. It's just that simple.