In today's video, we're going to be looking at all the different types of numbers that you need to know about, and we can split them into two different groups. Those that are rational, like integers, fractions, and terminating or recurring decimals, and those that are irrational, like certs. So in this video, we'll go through them one by one, and look at some examples of each.
If we start with integers, this is just another name for a whole number. So it could be a positive whole number like 5, 13, or 412, or it could be a negative number like minus 11 or minus 92. As long as it's a whole number, then it counts as an integer, and 0 also counts as an integer. In contrast to this, fractions are only parts of a whole number, and we write them as one integer, like 3, over, or divided by, another integer, for example, 8, which in this case would give us 3 8ths.
To put this into practice, if you had a pizza, and you cut it up into 8 equal slices, you'd have divided it by 8. And if somebody then ate three of those slices, they'd have eaten three eighths of the pizza, or eaten three over eights. And so you'd be left with five eighths of the pizza, because you only have five of those eight slices left. The other important thing to know about fractions is that we have special names for these two numbers.
The top number is called the numerator and the bottom one is the denominator. Now terminating and recurring decimals are both examples of rational numbers but they are two different things and you need to understand what that difference is. Terminating decimals are numbers like 0.5 or 0.625. which have a limited number of decimal places. For example, 0.5 only has one decimal place, which is the 5, and 0.625 has three decimal places, the 6, the 2, and the 5. In contrast, recurring decimals continue indefinitely, like 0.66666 going on forever.
We obviously don't want to write out an infinite number of sixes though, so instead you can put a dot above the digit that occurs. So for this one you could just write out 0.6 and then put a little dot just here above the six to show that it's the six which is occurring. For more complicated ones like zero point one two three one two three one two three and so on it's the whole 1, 2, 3 part which is recurring.
So we place the dots above the 1 and the 3, because the 1 is the first number that recurs and the 3 is the last number that recurs. Or as another example, in this number it's the 4781 which is recurring. So we could rewrite it as 0. four seven eight one and then place dots above the four and the one. Another thing you need to be aware of is that because terminating and recurring decimals are both examples of rational numbers we can write them in a fraction form as well.
For example 0.5 is the same thing as one half and 0.625 is five eighths. then 0.6 recurring equals two thirds, and 0.123 recurring equals 123 over 999. Now the last thing we need to cover are irrational numbers, which are much harder to write because their decimals continue forever. but they don't repeat, so they look like a random string of numbers going on forever. The main place you'll see irrational numbers are thirds, which we cover in detail in another video, but are basically square roots of non-square numbers, like the square root of 2, which would be something like 1.414213, but would continue on forever without any pattern.
In contrast, if we square root a number like 9, then that doesn't count as a third, because 9 is a square number, and we can simplify square root 9 to 3. Another example of an irrational number is pi, which would be somewhere on your calculator, and starts as 3.14159, but again, goes on forever, and doesn't have any pattern. So to sum up this video, a rational number is basically any number that has a limited number of decimal places and can be written as a fraction, whereas irrational numbers are those that continue on forever and so to write them down we always have to round them. Anyway that's everything for this video so hope you found it useful, if you did then be sure to give us a like and subscribe and we'll see you in the next video.