In base 2, 19 is 10011. In base 1/2, 19 is 1.1001
In base 10, 19 is 19. In base 1/10, 19 is 9.1
The trick is to write the number in reverse, and in the fractional version, put a decimal point after the ones column. This is because decimals have negative exponents, so the fraction gets flipped.
Fractional bases that aren't 1/something seem like a real mess to use.
Also, I wanted to count in balanced base 3. I will use -, 0, and + for my digits.
+ +- +0 ++ +-- +-0 +-+ +0- +00 +0+
You'll notice that you *can* count be incrementing the one's column repeatedly. You just have to remember to reset things to - not 0, after they overflow.
Will count from -1 to -5 now:
- -+ -0 -- -++
Notice it's the same as positive, with the -'s and +'s reversed, and 0's untouched. And you can count by decrementing the one's column, and when it overflows, decrement the next column and reset things to a +. I guess I should point out that you can add as many leading zeroes as you want, which is how decrementing a column that doesn't exist works.