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.
