Connecting Repeating Decimals to Undergraduate Number Theory Through the Use of Calculators

Abstract

In this session, we will report on how we use calculators to help college students and prospective teachers to explore decimal expansions of fractions (that is, rational numbers). When we deal with real numbers we are actually dealing with decimal expansions, because real numbers are represented by decimal expansions. However the concept of decimal expansions is neglected in schools. The reason is that finding the decimal expansion with paper and pencil is tedious work. But now with the help of technology finding the decimal expansions of those real numbers that are rational is easy and fun, and there are interesting and challenging questions that can be pursued. The author has long been interested in how technology can be used to enhance mathematics teaching and learning. We give some general background on curriculum thinking about educational use of technology. We then describe some specific activities involving decimal expansions that we believe will help students achieve a better understanding of this important topic.