To multiply the two numbers in scientific notation \(5.5 \times 10^4\) and \(2.2 \times 10^{-8}\), 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: \[ 12.1 \times 10^{-4} \]
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Convert to proper scientific notation: In scientific notation, the coefficient should be between 1 and 10. To convert \(12.1\) to proper scientific notation, you move the decimal point one place to the left, which increases the exponent by 1:
\[ 12.1 \times 10^{-4} = 1.21 \times 10^{-3} \]
So the answer in scientific notation is:
\[ \boxed{1.21 \times 10^{-3}} \]