This Instructional Activity is a part of the Lesson 11, Unit 7, Grade 8. We have seen thus far that numbers whose decimal expansions are infinite and do not repeat (Lesson 8) are irrational. We saw from the last lesson what kinds of numbers (fractions with denominators that are a multiple of or simplified multiple of ) produce decimals expansions that are infinite but repeat. What kind of number produces a decimal expansion that is both infinite and non repeating? The lesson investigates the decimal expansions of non-perfect squares.