This Instructional Activity is a part of the Lesson 10, Unit 7, Grade 8. Students develop a convincing argument establishing that every real number with a repeating decimal is a rational number. In Lesson 8, we say that every rational number, that is, every fraction, has a decimal expansion that falls into a repeating pattern. A natural question now is the converse: If a real number has an infinitely long decimal expansion with a repeating pattern, must it be a rational number?
