. Grade 8, Illustrative icon
Task

Identifying Rational Numbers

Illustrative MathematicsVaries

The task assumes that students are able to express a given repeating decimal as a fraction. There is a lot of interesting mathematics behind deciding questions about irrationality. There are a variety of arguments demonstrating that is irrational (some of which would be quite accessible to a motivated middle school student), the first of which were discovered somewhere around the 5th century BC.

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