Improper fractional base
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An improper fractional base is a type of number base. Instead of using an integer for the base in our positional number system, we use an improper fraction for the base.
The usual methods of converting from base 10 to another base do not work for improper fractional bases: most integers, when we convert them using this method, have an infinite representation in an improper fractional base. (Note that this means there is not a unique representation for each number in an improper fractional base.)
Improper fractional bases were first discovered by A. J. Kempner in 1936, but were not investigated deeply.