A common algorithm for converting a decimal number that is between 0 and 1 to binary is to multiply by 2 and record the integer part of the result. Then, you subtract that integer from the result and repeat the process.
Example = ${0.1}_{10} = \frac{1}{10}$
Result = ${0.0 0011 0011 0011...}_2$
Is there any simple way to tell the maximum repeating period of a binary fraction obtained using that conversion algorithm?