Repeating Binary Expansions

All rational numbers have repeating binary expansions. Operations to access the individual bits of a binary expansion can be obtained by converting the value to RadixExpansion(2). More examples of expansions are available in DecimalExpansion, HexadecimalExpansion, and RadixExpansion. The expansion (of type BinaryExpansion) of a rational number is returned by the binary operation.

Arithmetic is exact.

The period of the expansion can be short or long...

or very long

These numbers are bona fide algebraic objects.