Question regarding digits in base 2

[GridironCPJ]

Suppose we have a decimal string in base 2 (ex: 0.10111000...) then are there any of these that equal the same number in [0, 1]? I was never formally introduced to anything like this, yet I'm being asked questions involving base 2, base 3, etc. If someone could answer this, it would help me solve a problem involving such a fact.

 

[Infinitum]

Perhaps, you want to know how to change base from 2 to decimal?

http://mathbits.com/mathbits/compsci/Introduction/frombase10.htm

http://www.mathpath.org/concepts/Num/frac.htm

From that, can you conclude whether they can be same??

 

[HallsofIvy]

Just as, in base 10, 0.9999...= 1 so, in base 2, 0.11111...= 1.

Similarly, in base 10, 0.49999...= 0.5 and, in base 2, 0.0111...= 0.1 and so forth.