Rational numbers

One, two, three, four. Four cows, two children, one bucket. It feels natural to count like this, nd this is exactly what we call these numbers - the natural numbers. A capital "N" is used to describe the set of natural numbers. In Sweden we usually include zero in the set of natural numbers, but not all mathematicians agree on that.

On a number line, natural numbers lie to the right from zero. To the left from zero we have negative numbers. It can feel strange to think about negative numbers - you can't have minus four cows. You can, however, owe a friend money - you can then have minus ten kronor. Natural numbers, zero, and negative numbers are called whole numbers.

We use a capital "Z" to describe this set of numbers. It comes from the German word for number, "Zahl" If we look closer, we can see that there are spaces between the whole numbers on the number line. Here is an example: "one half" And between a half and one is three quarters. And if we continue between three quarters and one, there's seven eighths for example. If we zoom in even more, we can keep adding as many fractions as we want - an infinite number of them, actually.

Between any two numbers on the number line, there is an infinite number of fractions. All numbers that can be written as fractions are called rational numbers. Rational usually means that you are logical or sensible. It comes from the Latin word ratio, which means calculation or relation. And a rational number is exactly that - a relation between a numerator and a denominator, or a fraction.

The fact that all fractions are rational numbers means that even whole numbers are part of the set of rational numbers, as they can also be written as fractions. Two, for example, can be written as eight quarters. And minus three can be written as minus nine thirds. The set of rational numbers is denoted by a "Q", from the Latin word quotus, which means quotient. Quotient is the result of the division of the numerator by the denominator.

One more thing about rational numbers: Fractions cannot have zero in the denominator. A number divided by zero is undefined, but that is another story. The set of rational numbers includes whole numbers, and the set of whole numbers includes natural numbers. Like this: Five is a natural number, a whole number and a rational number. Minus two is a rational number and a whole number, but it is not a natural number.

So, it goes to the middle circle. Two thirds is a rational number, but it is neither a natural or a whole number. So, it goes to the outer circle. Was that easy? Check out the video on irrational numbers.

That's where things get really interesting.