To divide \( 3.3 \times 10^4 \) by \( 5.5 \times 10^7 \), you can separately divide the coefficients and the powers of ten.
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Divide the coefficients: \[ \frac{3.3}{5.5} = 0.6 \]
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Divide the powers of ten: \[ \frac{10^4}{10^7} = 10^{4-7} = 10^{-3} \]
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Combine the results: \[ 0.6 \times 10^{-3} \]
This can also be expressed in scientific notation as: \[ 6.0 \times 10^{-4} \]
Thus, the final result is: \[ \boxed{6.0 \times 10^{-4}} \]