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Even if you filled in all the rational numbers, you’d still have points left unlabeled on the number line. These points are the irrational numbers.

An irrational number is a number that’s neither a whole number nor a fraction. In fact, an irrational number can only be approximated as a non-repeating decimal. In other words, no matter how many decimal places you write down, you can always write down more; furthermore, the digits in this decimal never become repetitive or fall into any pattern. (For more on repeating decimals, see Chapter 13.)

The most famous irrational number is π (you find out more about π when I discuss the geometry of circles in Chapter 19):

Together, the rational and irrational numbers make up the real numbers, which comprise every point on the number line. In this book, I don’t spend too much time on irrational numbers, but just remember that they’re there for future reference.