Example 5: Fractions Represent Terminating or Repeating Decimals

This Instructional Activity is a part of the Lesson 14, Unit 2, Grade 7. The long division algorithm either terminates with a zero remainder or the remainder repeats. How do we determine whether the decimal representation of a quotient of two integers, with the divisor not equal to zero, will terminate or repeat? In the division algorithm, if the remainder is zero, then the algorithm terminates, resulting in a terminating decimal.