To multiply the numbers \( 5.5 \times 10^4 \) and \( 2.2 \times 10^{-8} \), follow these steps:
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Multiply the coefficients: \( 5.5 \times 2.2 = 12.1 \)
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Add the exponents of the powers of ten: \( 10^4 \times 10^{-8} = 10^{4 + (-8)} = 10^{-4} \)
Putting it all together, we have: \[ 12.1 \times 10^{-4} \]
Now, to express this in proper scientific notation, we need the coefficient between 1 and 10. Therefore, we rewrite \( 12.1 \) as \( 1.21 \times 10^1 \).
Now, combining this with \( 10^{-4} \): \[ 1.21 \times 10^1 \times 10^{-4} = 1.21 \times 10^{1 - 4} = 1.21 \times 10^{-3} \]
Thus, the final answer in scientific notation is: \[ \boxed{1.21 \times 10^{-3}} \]
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