Relationship Between Decimal Numbers and Fractions

One of the clearest ideas to most readers is the idea that decimal numbers and fractions are interrelated. We have had numerous experiences in school in which we have translated back and forth between these two representational systems. Familiar to all of us is the idea that ½ = 0.5 = one-half. We can easily recall that 0.1 can be read as "one-tenth," as can 1/10. We know well that 0.25 is the same amount as ¼. With a little thought we can probably remember learning to express remainders in division problems first of all as whole numbers (remainder 4, for example), then as fractions, and eventually as decimal numbers.

What we need to begin to consider here is the idea that everything that we have learned about fractions can be translated in some way into a decimal number context. It is not just a matter of being able to convert or translate from fractions to decimals (or vice versa), but rather, it is a matter of seeing fractions and decimals as two different representational systems for essentially the same underlying ideas. Not only are the two systems interrelated, but the conceptual basis for both systems is virtually the same. We are interested in far more than skill of translating between the two systems using memorized procedures. Rather, we are concerned about developing an understanding of the underlying concepts and the way in which both systems relate to those underlying concepts.