This sub topic is about the 4 key sets of numbers that define our number system. Natural numbers, Integers, Rational numbers and Real numbers. This section starts by taking you through the concept of number sets, starting with sets that we have been using for years, like even numbers. Then there is a little about how the sets have evolved followed by some key definitions of the four sets and example of how they fit together. Then, as usual, the section finishes with some revision exercises asnd examples of how this concept is tested.
What are sets of numbers?
Defining the sets and subsets!
In the video below, you will get some clear definitions of the 4 subsets and how they fit together this should help you to be clear about these key properties of numbers and how to classify them.
Revise
This section offers a brief summary of the key points and then a quiz to help you check that you know what you need to know. Click the 'hidden box symbol' to see this section
Read through and check the following flashcards. You can come back to these as often as you like.
Gallery
Complete all of the questions in the following quiz before checking your answers. Check how you did and then read the help offered for any questions you didn't get. You can redo the quiz at anytime to check yourself. (The order of the answers is reshuffled when the page is reloaded)
1
Which of the following best describes the set of natural numbers?
The set of Natural numbers is all positive, whole numbers. This does not include any negative numbers or fractions.
2
Which of the following best describes the set of rational numbers?
Rational numbers are all the numbers that be expressed as whole. This includes all of the integers because they can all be expressed as fractions too. eg . Not all decimals can be expressed as fractions. Irrational numbers are decimals whose places go on infinitely without any discernable pattern, so that cannot be expressed as fractions.
3
Which of the following statements are true about the set of irrational numbers ?
Not all decimals can be expressed as fractions. Irrational numbers are decimals whose places go on infinitely without any discernable pattern, so that cannot be expressed as fractions.
All rational numbers are real, but not the other way around.
4
Which of the following statements are true?
Check the subsets digram to review these statements
5
Which of the following sets does 45.643 belong in?
45.643 is neither natural or an integer because it is not a whole number
6
Which of the following sets does belong in?
Integers
is neither natural or an integer because it is not whole. It is also not rational beacuse it cannot be expressed as a fraction
7
Which of the following numbers are rational but not integers
All of the 'whole' numbers are excluded and 23.5 x 104 = 235000 which is also whole.
8
Which of the following diagrams shows the correct arrangement of the four main subsets?
Diagram C is the correct diagram because it shows, correctly, that all natural numbers are integers, all integers are rational and that all rational numbers are real.
9
Is the following table correctly filled in?
is irrational and therefore only real. 7 is natural and therefore everything else. -6.1 is part of a number and negative so not an integer and not natural, but is a terminating decimal so it can be expressed as a fraction, so it is rational. Likewise is rational and therefore real.
10
Which of the following is the most comprehensive description of the set that 3.456 x 103 is in?
The answer is 'Natural' because if a number is natural then it is also a real, rational integer!
Practice questions
This section will go through a couple of exam style questions on this topic. Click the 'hidden box symbol' to see this section
Question 1
Question 2
MY PROGRESS
How much of Prior Knowledge - Sets of Numbers have you understood?
Feedback
Which of the following best describes your feedback?
The four subsets
. Not all decimals can be expressed as fractions. Irrational numbers are decimals whose places go on infinitely without any discernable pattern, so that cannot be expressed as fractions.
belong in?
is irrational and therefore only real. 7 is natural and therefore everything else. -6.1 is part of a number and negative so not an integer and not natural, but is a terminating decimal so it can be expressed as a fraction, so it is rational. Likewise 
is rational and therefore real.
Twitter 
Facebook 
LinkedIn