To multiply the numbers in scientific notation, you can separate the coefficients and the powers of 10.
Given: \[ (5.5 \times 10^4) \times (2.2 \times 10^{-8}) \]
First, multiply the coefficients: \[ 5.5 \times 2.2 = 12.1 \]
Next, multiply the powers of 10: \[ 10^4 \times 10^{-8} = 10^{4 + (-8)} = 10^{-4} \]
Now, combine the results: \[ 12.1 \times 10^{-4} \]
However, the coefficient 12.1 needs to be converted into proper scientific notation, where the coefficient is between 1 and 10. To do this, we can express 12.1 as: \[ 12.1 = 1.21 \times 10^1 \]
Substituting this back, we have: \[ (1.21 \times 10^1) \times 10^{-4} = 1.21 \times 10^{1 - 4} = 1.21 \times 10^{-3} \]
Thus, the final answer in scientific notation is: \[ \boxed{1.21 \times 10^{-3}} \]