AQA · Mathematics · 8300
GCSE Maths: Number: rational/irrational
Number · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Number: rational/irrational (Corbettmaths Video 230), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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Are all integers rational numbers?
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Yes. Every integer can be expressed as a fraction (e.g., 5 = 5/1), so all integers are rational.
Is a recurring decimal a rational or irrational number?
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Rational. All recurring decimals can be expressed as fractions, so they are rational numbers.
Is 0.3333... (recurring) a rational number?
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Yes. It is rational because it is a recurring decimal and can be expressed as a fraction (1/3).
Is π (pi) a rational or irrational number?
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Irrational. π cannot be expressed as a fraction of two integers.
What type of number results when you multiply (7 − √2)(7 + √2)?
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Rational. The product equals 49 − 2 = 47, which is an integer and therefore rational.
Can two surds multiply together to give a rational answer?
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Yes. For example, √2 × √2 = 2, which is rational. Surds can multiply to give rational numbers.
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