Learning objective
Irrational numbers: Be familiar with the concept of an irrational number. An irrational number is one that cannot be written as a fraction, for example √2.
Read the explanation, check the common trap, then practise with flashcards and questions.
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Topic
Number systems
Subtopic
Irrational numbers
Study support
Understand this objective
Quick explanation
Irrational numbers: Be familiar with the concept of an irrational number. An irrational number is one that cannot be written as a fraction, for example √2
- This point belongs to Number systems, especially Irrational numbers.
- You need to be able to irrational numbers: Be familiar with the concept of an irrational number. An irrational number is one that cannot be written as a fraction, for example √2.
- Use the linked flashcards and practice questions to check recall, then practise applying the idea in an exam-style answer.
Why it matters
This objective helps connect Irrational numbers to exam-style questions, flashcards, and revision notes for Number systems.
Quick student answer
Which statement best describes an irrational number?
Direct answer
A number that cannot be written as a fraction
Key terms
- Irrational number: A number that cannot be written as a fraction.
- Fraction: A way of writing a number using a numerator and denominator, such as 1/2.
Common trap
Confusing notation with classification: Use the defining test: an irrational number cannot be written as a fraction. √2 is an example.
Related questions
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Flashcard prompts
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Revision tools
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Practice Questions0 linked questions
Related learning objectives
- Natural numbers: Be familiar with the concept of a natural number and the set ℕ of natural numbers (including zero). ℕ = {0, 1, 2, 3, … }
Natural numbers
- Integer numbers: Be familiar with the concept of an integer and the set ℤ of integers. ℤ = { …, -3, -2, -1, 0, 1, 2, 3, … }
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- Rational numbers: Be familiar with the concept of a rational number and the set ℚ of rational numbers, and that this set includes the integers. ℚ is the set of numbers that can be written as fractions (ratios of integers). Since a number such as 7 can be written as 7/1, all integers are rational numbers.
Rational numbers
- Real numbers: Be familiar with the concept of a real number and the set ℝ of real numbers, which includes the natural numbers, the rational numbers and the irrational numbers. ℝ is the set of all 'possible real world quantities'.
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- Ordinal numbers: Be familiar with the concept of ordinal numbers and their use to describe the numerical positions of objects. When objects are placed in order, ordinal numbers are used to tell their position. For example, if we have a well-ordered set S = {‘a’, ‘b’, ‘c’, ‘d’}, then ‘a’ is the 1st object, ‘b’ the 2nd, and so on.
Ordinal numbers