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Decimal Expansions

Chapter
Part of the Undergraduate Texts in Mathematics book series (UTM, volume 0)

Abstract

Our goal in this chapter is to prove that every real number can be represented by a decimal and that every decimal represents a real number. Before You Get Started. In Chapter 7 we discussed base-ten representation of integers. In fact, all real numbers can be given base-ten representations: this is what you called “decimals” in grade school. Do you remember repeating and nonrepeating decimals? For example, the decimal expansion 0.1111... is supposed to represent the number \(\frac {1}{9}.\) Why is this a valid expression for \(\frac {1}{9}\) ? What is a decimal expansion of \(\frac{1}{8}\ {\rm or}\ \sqrt 2 ?\)

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Copyright information

© Matthias Beck and Ross Geoghegan 2010

Authors and Affiliations

  1. 1.Department of MathematicsSan Francisco State UniversitySan FranciscoUSA
  2. 2.Department of Mathematical SciencesBinghamton University State University of New YorkBinghamtonUSA

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