Decimals as Addresses

Purpose To show that the notion of geometric addresses, developed in our study of IFS, can be adapted to provide a visual interpretation of decimals illuminating some troublesome properties of decimals, for example, why 0.199999 ... = 0.200000 ... .
Materials Paper and pencil, a ruler with an inch and a centimeter scale
Background
Procedure Use a ruler to subdivide a line segment into pieces of a given length. Attach an address to each piece. Subdivide each of these pieces in the same fashion. Attach an address to each of these smaller pieces.
Sample For the sample we use the centimeter scale; for the exercise we use the inch scale because this allows a greater number of subdivisions without eye strain.
Conclusion
Exercises