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edX

Irrational Numbers

via edX

Overview

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Explore the real number system, beginning with rational numbers, fractions, and terminating decimals. Use long division and simplification to move between fractional and decimal forms.

Examine repeating decimals and apply algebraic methods to convert them into exact fractions. Learn how nonterminating, nonrepeating decimals define irrational numbers and recognize examples involving square roots, π, and e.

Develop practical estimation skills by rounding irrational values, testing squares, bounding square roots between integers, and plotting numbers on a number line. This beginner path is designed for learners seeking a stronger foundation in number systems and numerical reasoning.

Syllabus

  • Convert fractions into terminating or repeating decimals
  • Express terminating and repeating decimals as simplified fractions
  • Distinguish rational numbers from irrational numbers
  • Recognize and interpret repeating-decimal notation
  • Identify irrational values involving square roots, π, and e
  • Bound and approximate irrational numbers using integers and decimals
  • Compare and order real numbers on a number line

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