To divide \(3.3 \times 10^4\) by \(5.5 \times 10^7\), we can separate the coefficients and the powers of ten:
\[ \frac{3.3 \times 10^4}{5.5 \times 10^7} = \frac{3.3}{5.5} \times \frac{10^4}{10^7} \]
First, let's calculate the division of the coefficients:
\[ \frac{3.3}{5.5} = 0.6 \]
Next, we'll calculate the powers of ten:
\[ \frac{10^4}{10^7} = 10^{4 - 7} = 10^{-3} \]
Now, we can combine the two results:
\[ 0.6 \times 10^{-3} \]
To express \(0.6\) in scientific notation, we can write it as:
\[ 6 \times 10^{-1} \]
So we multiply:
\[ 6 \times 10^{-1} \times 10^{-3} = 6 \times 10^{-4} \]
Thus, the final answer is:
\[ \boxed{6 \times 10^{-4}} \]