To multiply the numbers in scientific notation, you can multiply the coefficients (the numbers in front) and then add the exponents of the powers of ten.
So, for \( 5.5 \times 10^{4} \) 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: \[ 4 + (-8) = 4 - 8 = -4 \]
Putting it all together, we get: \[ 12.1 \times 10^{-4} \]
Now, to express this in proper scientific notation, we need to have the coefficient between 1 and 10. Therefore, we can rewrite \( 12.1 \times 10^{-4} \) as: \[ 1.21 \times 10^{−3} \]
So the answer in scientific notation is: \[ \boxed{1.21 \times 10^{-3}} \]