How to convert an infinite binary fraction into a decimal fraction

Question

I am asked to write the infinite binary fraction $0.(1011)$, where the $1011$ is the repeating part, as a $\frac pq$ fraction.

What are the steps to do this?

EDIT:

If $0.(1011)$ was in base 10, I could write it as $\frac {337}{3333}$... hmm how can this help?

EDIT EDIT: got it now :) it's $\frac {11}{15}$

Answer 1

Hint: You can do the same as you do for converting a repeating decimal to a fraction. As the repeat has four bits, multiply by $2^4$ and subtract the original. All the repeating bits will disappear. Can you see the link to the sum of a geometric series?

Answer 2

HINT:

$$(\cdots B_1B_0.b_0b_1\cdots)_r=\cdots r^1\cdot B_1+r^0\cdot B_0+b_0\cdot r^{-1}+b_1\cdot r^{-2}\cdots$$