To clarify the idea I shall explain what I mean.
The current number systems deals with numbers in the form of tens (10s) , meaning that every 10 units in the ones unit equal 1 unit in the tens unit. I shall talk about a system that is a bit different, a system that deals with numbers in the form of twoes (2s) , every 2 units in the ones unit equal 1 unit in the twoes unit. So the system looks like the binary system. But we shall extend this system to include decimal numbers, each decimal after the point is half the value of the previous unit. For example the number 0.1 in our binary-like system is equal to 0.5 in the tens system. And 0.01 is equal to 0.25, and so on.
My question is , is a number like 0.251 possible to be reached in the binary-like number system and be represented by a finite number of digits ? if not, then what is the resulted number that we get from trying to reach it, is it a continuous fraction repeating itself, or a transcendental number not repeating itself ?