To multiply the numbers in scientific notation, you will multiply the coefficients and add the exponents of the powers of ten.
Given: \[ 5.5 \times 10^4 \text{ and } 2.2 \times 10^{-8} \]
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Multiply the coefficients: \[ 5.5 \times 2.2 = 12.1 \]
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Add the exponents: \[ 4 + (-8) = 4 - 8 = -4 \]
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Combine the results: \[ 12.1 \times 10^{-4} \]
Since \(12.1\) is not in proper scientific notation (the coefficient should be between 1 and 10), we can convert it:
\[ 12.1 = 1.21 \times 10^1 \]
Now, we can rewrite the expression: \[ 1.21 \times 10^1 \times 10^{-4} = 1.21 \times 10^{1 - 4} = 1.21 \times 10^{-3} \]
Thus, the final answer in scientific notation is: \[ \boxed{1.21 \times 10^{-3}} \]