1. The problem statement, all variables and given/known data Imagine any recurring decimal in base 10, call it X. examples: .1111111111... .2222222222.... .23232323.... my question is - can you convert it to binary without rewriting X in fractional form. I know how to do it in fractional form. I know how to convert it to fractional form as well. However, I'm curious if one can proceed to solve this problem without converting to fractional form like a/b where a and b are integers. 2. Relevant equations - divide/mult by 2 to convert integer/decimal part to binary 3. The attempt at a solution The reason I ask this is because I know (and can) convert recurring decimals from binary to decimal. However, I'm not aware of any trick that does the other way around (w/o making use of fractions) and if there is one I would like to know how its done. Thanks.