Grade 10-11 · Numbers · 64 pages · PDF

Rational and Irrational Numbers

Clear, exam-focused notes on the number system, rational and irrational numbers, and converting recurring decimals to fractions, with fully worked examples.

A concise 14-page IGCSE guide to rational and irrational numbers. It starts with the real number system and how natural numbers, integers, rational numbers and irrational numbers fit together. It then explains what makes a number rational, with a step-by-step method for converting recurring decimals to fractions (including those where only part of the decimal recurs). It also covers how to identify irrational numbers such as surds and π, and what happens when you add or multiply rational and irrational numbers. Every method comes with worked examples and common mistakes to avoid. It ends with a summary table, a quick classification test and exam tips.

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• Cheatsheet · 2 pages

  Cheatsheet

  The whole topic on a page or two, for the night before.

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• Worksheet · 25 pages

  Worksheet

  Practice questions in the order the notes teach them.

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• Solutions · 22 pages

  Solutions

  Every worksheet question worked in full.

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• Main Notes · 15 pages

  Main Notes

  The full notes: one idea per page, a worked example beside every rule.

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Topics covered

• The real number system
• Natural numbers, integers and rational numbers
• What makes a number rational?
• Terminating and recurring decimals
• Converting recurring decimals to fractions
• What makes a number irrational?
• Square roots of non-perfect squares
• Classifying numbers as rational or irrational
• Operations with rational and irrational numbers
• Summary and exam tips

Format

Print-ready PDF

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4

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