2.
Powers of Three
I first ran across the fraction 1/243 in one of the Rama series of books by
Arthur C. Clarke. Now 243 is the fifth power of 3. The decimal equivalent forms
a very curious pattern as I describe in the notes. I then created an Excel
spreadsheet to calculate decimal equivalents of the reciprocals of different
powers of three to help analyze the patterns ( the notes explain how to create
this spreadsheet ). I then could extend the work to explore powers of other
repeating decimals. The only limitation is the size of your spreadsheet and your
imagination.