Expanding the Limits of the Calculator Display

Abstract

The decimal expansions of 1/7 or 5/13 can be found immediately on the average electronic calculator. These decimal expansions are limited to six digits before they begin to repeat. But what do we say to students who want to explore the repeating properties of rational numbers? What would we answer if they asked for the decimal expansion of 1/17 or 3/23? Do we just say, “Keep dividing and you'll find the answer”? Hardly. Long decimal expansions are usually left to actuaries who don't want to mismanage thousands of dollars over the life of an annuity or mortgage table, or to spacecraft engineers who don't want to miss their targets in outer space.