GCSE Maths - Types of Numbers

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 occurring 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 three

over or divided by another integer for example eight which in this case would give us three eighths

to put this into practice if you had a pizza and you cut it up into eight equal slices you'd have divided it by eight

and if somebody then ate three of those slices they'd have eaten three eighths of the pizza or eaten a three over eight

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're 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 five

and 0.625 has three decimal places the six the two and the five 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

one two three one two three one two three and so on it's the whole one two three part which is occurring so we place the dots above the one

and the three because the one is the first number that occurs and the three is the last number that occurs

or as another example in this number is the four seven eight one which is occurring so we could rewrite it

as 0.4781 and then place dots above the 4 and the 1.

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 5 8.

then a 0.6 occurring 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 number like 9

then that doesn't count as assert because 9 is a square number and we can simplify square root 9 to 3.

another example of an irrational number is pi which will 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