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

In this paper, we will report on how we use calculators to help college students and prospective teachers to explore decimal expansions of fractions. Questions that come out of this exploration are; how many digits need to be calculated to completely determine this decimal number? Can we determine the decimal expansion by calculating finitely many digits? How can we tell if the displayed number in the calculator gives complete information about the expansion? In order to answer these and other questions, we design some specific activities which we believe will help students achieve a better understanding of decimal expansions. Our activities turn out to lead to more advanced topics in number theory. More broadly speaking, our paper is motivated by two questions related to using technology in teaching and learning mathematics: 1. How can technology be used to teach theoretical concepts? 2. How does technology change the content of mathematics