Task# Repeating or Terminating?

Illustrative MathematicsVaries

The purpose of this task is to understand, in some concrete cases, why terminating decimal numbers can also be written as repeating decimals where the repeating part is all 9's. Terminating decimals also have a more familiar 'repeating' representation where the repeating part is all 0's: for example 1/2 = 0.5000. Students can benefit from work on this problem in both the seventh and the eighth grade. In the seventh grade, the emphasis should be on checking that the mathematics in Sarah's calculations is correct and so 1 and 1/2 have both a terminating and an eventually repeating decimal expansion.