# Rational numbers

Rational numbers are a special type of number – some numbers are rational¸ some are not.  What makes a rational number?  Well, for a number to be rational, you need to be able to write it as a fraction with an integer on the top (numerator), and an integer on the bottom (denominator).  So, for instance, the number 3 is a rational number, because I can write it as a fraction like this:

There’s an integer on the top – ‘3’, and an integer on the bottom – ‘1’.  What about a slightly more complicated number like, 1.5?  Well, I can write this as a fraction with integers on the top and bottom as well, it’s just a slightly more complicated one:

Negative numbers can be rational numbers as well, they aren’t limited to only positive numbers.  Take –9 for instance, as a fraction I could write this:

## How Many Rational Numbers?

Lots and lots!  In fact there are an infinite number of rational numbers hanging around.  We can show this by thinking about how many rational numbers there are between 0 and 1.

is a rational number between 0 and 1.  So there’s at least one rational number between them.

and  are rational numbers as well.  So that’s another two rational numbers between 0 and 1 – that makes 3 all up.

, ,,… all the way to  are rational numbers, and they’re between 0 and 1.  So that’s a whole lot more…

, , ,… all the way to  are rational numbers between 0 and 1, so that’s even more.

You can keep doing this forever, there’s always another rational number you can think of.  Think you’ve thought of all of them?  What about ?  It’s a rational number, and it’s between 0 and 1.  There are an unlimited number of rational numbers.

### Zero is a rational number

To be rational, you need to be able to write the number as a fraction with an integer on the top and an integer on the bottom.  You can write zero as a fraction this way:

or  or

Zero is an integer.  If you put zero on the top of the fraction, you can divide it by any integer, and you’ll always get zero as an answer.