Question

What is 5.5 x 10 to the fourth power multiplied by 2.2 x 10 to the negative eighth power? Write the answer in scientific notation.

Answer 1

To multiply the numbers in scientific notation, you can separate the coefficients and the powers of 10.

Given:
\[
(5.5 \times 10^4) \times (2.2 \times 10^{-8})
\]

First, multiply the coefficients:
\[
5.5 \times 2.2 = 12.1
\]

Next, multiply the powers of 10:
\[
10^4 \times 10^{-8} = 10^{4 + (-8)} = 10^{-4}
\]

Now, combine the results:
\[
12.1 \times 10^{-4}
\]

However, the coefficient 12.1 needs to be converted into proper scientific notation, where the coefficient is between 1 and 10. To do this, we can express 12.1 as:
\[
12.1 = 1.21 \times 10^1
\]

Substituting this back, we have:
\[
(1.21 \times 10^1) \times 10^{-4} = 1.21 \times 10^{1 - 4} = 1.21 \times 10^{-3}
\]

Thus, the final answer in scientific notation is:
\[
\boxed{1.21 \times 10^{-3}}
\]