The decimal expansion of most common fractions will result in a set of digits that eventually repeat themselves. The number of digits in each set can vary from 1 to (denominator-1). These periodic sequences of digits have many curious properties, not all of them as predictable as one might suppose. In order to observe these properties it is necessary to have available an ample number of examples. These can readily be generated using one or other of the of the programs provided here. A separate program is provided to sort the sequences by length. This is just one possible way in which further work might progress. Obviously there is plenty of scope here for development.
Curiously, these sequences sometimes hint at unsuspected links with apparently unrelated branches of Number Theory. A variety of algorithms can be devised to express recurring decimals by the summation of infinite series. A particularily interesting aspect is the intimate relationship that can be established between recurring decimal sequences and the Fibonacci Series. A good introduction to all this can be found in 'NUMBERS' by L. F. Taylor, published by Faber & Faber in 1970.
An extensive listing of long repeating decimal sequences will provide a great deal of material with which to experiment.
