Number Systems Practice
Solve chapter-level practice questions for Number Systems with reveal-only solutions and quick revision support.
Practice Set 1 — Rational, Irrational, Decimals
Classifying numbers, converting recurring decimals, number line.
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Practice Set 2 — Surds and Exponents
Rationalising denominators and using the laws of exponents.
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Quick Q&A Before You Revise
Is every real number rational?
No. Every rational number is real, but numbers like √2 and π are real and irrational. Real numbers are the union of rational and irrational numbers.
Are the square roots of all positive integers irrational?
No. √4 = 2, √9 = 3, √25 = 5 are rational. Only the square root of a positive integer that is not a perfect square is irrational.
What does it mean to rationalise a denominator?
It means to rewrite the fraction so that its denominator has no surd (irrational root). We multiply the numerator and denominator by a suitable factor (often the conjugate).
Why is 0.101001000100001… irrational?
Its decimal expansion never ends and never settles into a repeating block (the number of zeros keeps increasing). A decimal that is non-terminating and non-recurring represents an irrational number.