Decimals as Addresses

We visualize decimals as successive gradations on a cm scale ruler.

We compute decimal expansions by iterating the process of dividing by 10.

The goal of this session is 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... .

First, to review format issues we examine a sample lesson plan on logarithms and dimensions. Sample lesson plan

Geometric addresses are more easily introduced with an inch scale ruler, so this is where we begin. Inch scale addresses

Addresses with a cm scale ruler are analogous to those with an inch scale ruler, except that at each level the cm scale has five times as many markings as the corresponding inch scale. Cm scale addresses

Here are a few basic questions that can be approapched using addresses. Basic questions

First, to review format issues we examine a sample lesson plan on logarithms and dimensions.	Sample lesson plan
Geometric addresses are more easily introduced with an inch scale ruler, so this is where we begin.	Inch scale addresses
Addresses with a cm scale ruler are analogous to those with an inch scale ruler, except that at each level the cm scale has five times as many markings as the corresponding inch scale.	Cm scale addresses
Here are a few basic questions that can be approapched using addresses.	Basic questions