Learning objective
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.
Read the explanation, check the common trap, then practise with flashcards and questions.
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Topic
Number systems
Subtopic
Rational numbers
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Quick explanation
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
- This point belongs to Number systems, especially Rational numbers.
- You need to be able to 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.
- 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 Rational numbers to exam-style questions, flashcards, and revision notes for Number systems.
Quick student answer
Which statement best describes a rational number?
Direct answer
A number that can be written as a fraction, or ratio, of two integers
Key terms
- Rational number: A number that can be written as a fraction or ratio of integers.
- ℚ: The set of rational numbers, including all integers.
Common trap
Assuming integers are not rational: Remember that 7 can be written as 7/1. Since it can be represented as a ratio of integers, it belongs to ℚ.
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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, … }
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- 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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- 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.
Irrational 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