# 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:

_{}

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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:

_{}

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.