Education Technology

Middle Grades Math: Repeating Decimals and Fractions

by Texas Instruments


  • Students will explore and predict patterns found in repeating decimals for select fractions.
  • Students will determine the repeating digit (or group of digits) for a repeating decimal.
  • Students will find repeating digits and use patterns in repeating decimals to determine equivalent fractions.


  • decimal representation
  • repeating decimal
  • repeating digits

About the Lesson

This lesson involves students exploring patterns in repeating decimals that represent fractions with denominators 9, 99, and 999.
As a result, students will:

  • Find the repeating decimal representation for select fractions.
  • Find fractions given select repeating decimal representations.