What is continuous or precise depends on the base you use. I can't think of any example in base 2, but I believe in base 3 you could represent numbers that have

What is continuous or precise depends on the base you use. I can't think of any example in base 2, but I believe in base 3 you could represent numbers that have infinite digits in base 10. If I'm not mistaken, 0.3333... would be 0.1 and 0.6666... would be 0.2. It probably gets nasty for a lot of simple base 10 numbers, so it isn't a good solution.