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.