I know that when converting a decimal number from base 10 to base 2, the result might be not terminating, even though the number is terminating in base 10.
For instance, 0.2 -> 0.0011 0011 0011 ...
Is the contrary possible ? That means, is there a non-terminating decimal number which, converted to base 2, is terminating ? I can't find any !
If yes, is there a method to find them ?
And by the way, what about irrational numbers ? Could an irrational number in base 10 become rational in base 2 or in another base ?