Recurring Decimals

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Recurring Decimals

Some fractions create decimals that repeat forever:

  • 1/3 = 0.333... Written as 0.3̇ (dot notation)
  • 1/6 = 0.1666... Written as 0.16̇
  • 2/7 = 0.285714285714... Written as 0.2̇85714̇

Terminating vs Recurring:

  • Terminating: Stops after finite decimal places (1/4 = 0.25)
  • Recurring: Repeats forever (1/3 = 0.333...)
  • Rule: A fraction in simplest form terminates if denominator has only factors of 2 and 5

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