Express one-third as a dyadic number

Question

Could anyone express one-third as a dyadic number? (I think it will be in the form of a series) Dyadic numbers are in the form $a/b^n$ where $b = 2$, so $1/2$, $1/4$ etc. are dyadic numbers.

Answer 1

Note that by geometric series summation we have $$ \sum_{k=1}^\infty \frac{1}{4^k} = \frac{1}{4} \cdot \frac{1}{1-1/4}= \frac{1}{4} \cdot \frac{4}{3} = \frac{1}{3}. $$

Answer 2

$$\frac{1}{3}=\frac{01_{2}}{11_2}=\frac{0.(01)_{2}}{0.(11)_{2}}=\frac{0.(01)_{2}}{1}=0.(01)_{2}$$