Module 5 · Place value and decimals · Lesson 23 of 39

Repeating decimals

Write a decimal that repeats forever with a bar.

In this lesson · about 8 minutes

  • Recognize a repeating decimal
  • Write it with bar notation

Some fractions turn into decimals that never stop but repeat the same block of digits forever. 13 = 0.3333… and 611 = 0.545454…

We write these with a bar over the block that repeats: 0.3333… = 0.3 and 0.545454… = 0.54. If some digits come before the repeating part, they stay outside the bar: 0.1666… = 0.16.

Repeating decimals are rational, because they come from fractions.

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