Task# Repeating decimal as approximation

Illustrative MathematicsVaries

The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation. A formal explanation requires the idea of a limit to be made precise, but 7th graders can start to wrestle with the ideas and get a sense of what we mean by an 'infinite decimal.' Students can make observations which reinforce the topic at hand as well as lay groundwork for later developments. This task allows students to engage in standard for mathematical practice 8, Look for and express regularity in repeated reasoning.