What is a Rational Number? | Math Review
Rational numbers can be separated into four different categories: Integers, Percents, Fractions, and Decimals. An integer is a whole number (this includes zero and negative numbers), a percent is a part per hundred, a fraction is a proportion of a whole, and a ‘decimal’ is an integer followed by a decimal and at least one digit.
In math we have rational numbers and we have irrational numbers. We are taking a look at rational numbers which have four different categories, and those are integers, percentages, fractions and decimals.
We’re going define each of these, even if you’re already somewhat familiar with them we’re going to go ahead and define them and give some examples. Starting out with integers, an integer is a positive or negative whole number or a zero. 9 would be a whole number, it would be an integer because it’s a positive whole number.
-6 is an integer because it’s a negative whole number. Then, of course, 0 is an integer because we said it was. Now we move on to percents, which is kind of a more complicated way to say percent is a part per hundred.
An example of a percent is 20 percent, which we could also write as 20 parts per 100. The important thing here is that you know what a percent is, like 20 percent. Fractions, which is a proportion. An example would be 20 divided by 10, or 2 divided by 4.
Of course, we have decimals, so this is where we have an integer. Maybe 1, maybe 89, maybe 0. We have a decimal place, and then we have numbers after the decimal like 20.53. We have our integer, we have a decimal, and then we have numbers after the decimal.
Integers, percents, fractions, and decimals are all rational numbers, usually. There are some rules, so in order to be a rational number, just to summarize, it either has to be an integer -like we talked about- if it’s a number like 9, -6, 0 it’s always going to be a rational number. It gets more complicated when we come to fractions and decimals.
If it’s a fraction it has to be an integer divided by an integer, and this integer cannot equal 0. It’s an integer divided by an integer, so 7 divided by 4 cuts it, that works. Now decimals are a little bit more complicated because it either has to be a terminating decimal or a repeating decimal.
An example of a terminating decimal would be something like 2 divided by 4, from that you get 0.5. and it ends right there at the 5. A repeating decimal you do 1 divided by 3 and you get 0.3333, it goes on forever but notice you are getting the same number every time.
Really you could erase all these 3’s and just put a line over the 3 showing it’s a repeating decimal. What you don’t want is a decimal like pi where you have 3.14159265359, it just keeps going on and on – there is no ending to it – so it’s not a terminating decimal, and there’s no pattern to it, so it’s not a repeating decimal.
That’s what an irrational number is, one that just keeps going like this. These numbers they have basically a stopping point, and so that’s what we’re looking for. The reason I say that a fraction has to be an integer over an integer is because when you divide an integer by an integer you get a clean number, you get a decimal that is repeating or terminating.
When you start dividing a decimal or a fraction by a number, or a fraction by another fraction, that’s when you are going to start getting messy. If you’re wondering whether a fraction is a rational number, what you can do is go ahead and divide it out and then look at the decimal and decide whether it’s terminating, repeating or non-ending. And that’s how you determine if it is a rational number.