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## Repeating Decimals and Geometric Series

** Description:**This activity begins by reviewing conversions between fractions and decimals with an emphasis on repeating decimals. The formula for the partial sum of a geometric series is bypassed and students are directed to use find partial sums by using the “multiply, subtract, and solve” technique which mimics the derivation of the formula for the partial sum of a geometric series. This sets the stage for students to quickly find the fraction representation of a repeating decimal number. This activity would be well-suited as a prelude to introducing infinite and partial sums of geometric sequences.
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**Last Updated:**

**Subject(s):**- Mathematics
- Mathematics > Algebra

**Educational Level(s):**- College & Beyond

**Instructional Component Type(s):**- Activity: Experiment/Lab

- From: San Diego Area Knowledge Exchange for Developmental Math (SAKE)
- Contributed By: Theresa Gallo

This activity begins by reviewing conversions between fractions and decimals with an emphasis on repeating decimals. The formula for the partial sum of a geometric series is bypassed and students are directed to use find partial sums by using the “multiply, subtract, and solve” technique which mimics the derivation of the formula for the partial sum of a geometric series. This sets the stage for students to quickly find the fraction representation of a repeating decimal number. This activity would be well-suited as a prelude to introducing infinite and partial sums of geometric sequences. http://www.mathedpage.org/ copyright informaiton: http://www.mathedpage.org/rights.html