Here's another interesting phenomenon of repeating decimals.
We've explored repeating patterns for decimal expansions of such fractions as 1/7 (or other fractions with prime denominators larger than 7). What happens when the numerator is larger than 1? If you know the decimal representation of 1/7, is there an easy way to find the decimal representation of, say, 2/7?
One way would be to multiply the digits of the repeating part by 2. When we display the repeating parts in one or two rings, some interesting patterns emerge.
Use the following Interactive Activity to explore the repeating parts of decimal expansions for such fractions as 1/7, 2/7, ..., and 6/7 and 1/13, 2/13, 3/13, ..., and 12/13:
This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. For a non-interactive version of this activity, follow the instructions and complete Problem A16.