What Are Real Numbers? | Khan Academy Blog

What are real numbers?

When you hear the term “real numbers,” you might be thinking, “Well, aren’t all numbers real?” After all, whether you’re counting your apples, your dollars, or your followers on Instagram, those numbers are all quite real to you. But, in mathematics, “real numbers” has a very specific definition.

Real numbers are all the numbers that can be found on the number line. They include all the rational numbers (those that can be written as fractions, like 3/4 and -2/3) as well as all the irrational numbers (those that can’t be written as fractions, like pi and the square root of 2). Basically, any number you can think of that doesn’t involve the square root of a negative number is a real number.

Why do real numbers matter?

Now, if you’re anything like me, you might be thinking, “So what? Who cares?” And that’s a fair question. After all, most of us go through our entire lives without ever needing to know what a real number is. But, believe it or not, the concept of real numbers is actually pretty important in mathematics.

For one thing, mathematicians like to classify things. By understanding what makes a number “real,” they can understand the properties that all real numbers share. Additionally, the distinction between real and non-real numbers can be helpful when working with certain types of equations. For example, if you’re trying to solve an equation and you find that the answer is a square root of a negative number, you’ll know that the equation doesn’t have any real solutions.

So, while the concept of real numbers might not keep you up at night, it’s definitely worth knowing about. And if you ever find yourself at a really boring party, you can whip out this knowledge to try and impress people. Just don’t blame me if they all walk away.