Irrational numbers

Classify numbers — including surds, decimals, and π — as rational (can be written as a fraction of two integers) or irrational (cannot), justifying the classification.

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Te reo Māori terms

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Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

Terminology

  • rational number
  • irrational number
  • surd
  • pi (π)
  • e (euler's number)
  • terminating decimal
  • recurring decimal

Task goals

  • Classify a given number — an integer, decimal, surd, or π — as rational or irrational.
  • Identify which of several given numbers is irrational, or decide whether a general statement about rational/irrational numbers is true or false.
  • Determine which of two numbers, such as a surd and a decimal, is greater by estimating the surd's value.
  • Estimate between which two consecutive whole numbers a surd lies.
  • Put a mixed list of rational and irrational numbers (integers, surds, π) in ascending order.
  • Evaluate and correct a claim or misconception about rational versus irrational numbers, explaining the reasoning.

Key skills

  • Irrational numbers
  • Surds
  • Rational vs irrational

Quick stats

  • 81 total questions
  • 3 difficulty levels
  • Answers included