To multiply the two numbers in scientific notation, you can follow these steps:
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Multiply the coefficients: \[ 5.5 \times 2.2 = 12.1 \]
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Add the exponents: \[ 10^{4} \times 10^{-8} = 10^{4 + (-8)} = 10^{-4} \]
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Combine the results: \[ 12.1 \times 10^{-4} \]
Now, to express it in proper scientific notation, the coefficient should be between 1 and 10. Since \(12.1\) is not in that range, we can adjust it:
\[ 12.1 \times 10^{-4} = 1.21 \times 10^{1} \times 10^{-4} = 1.21 \times 10^{-3} \]
So, the final answer in scientific notation is:
\[ \boxed{1.21 \times 10^{-3}} \]