Question

Perform the indicated operations and give the answer in scientific notation.
StartFraction 3.6 times 10 Superscript negative 4 Baseline times 3.0 times 10 Superscript negative 3 Over 1 times 10 cubed times 2.4 times 10 Superscript negative 2 EndFraction
Question content area bottom
Part 1
Choose the correct answer below.
A.0.000000045
0.000000045
B.4.5 times 10 Superscript negative 8
4.5 times 10 Superscript negative 8
C.3.2 times 10 Superscript negative 8
3.2 times 10 Superscript negative 8
D.4.5 times 10 Superscript 18
4.5 times 10 Superscript 18

Answer 1

To perform the operation:

\[
\frac{(3.6 \times 10^{-4}) \times (3.0 \times 10^{-3})}{(1 \times 10^3) \times (2.4 \times 10^{-2})}
\]

First, calculate the numerator:

\[
3.6 \times 3.0 = 10.8
\]

And for the powers of ten:

\[
10^{-4} \times 10^{-3} = 10^{-4 -3} = 10^{-7}
\]

Thus, the numerator is:

\[
10.8 \times 10^{-7}
\]

Next, calculate the denominator:

\[
1 \times 2.4 = 2.4
\]

And for the powers of ten:

\[
10^{3} \times 10^{-2} = 10^{3 - 2} = 10^{1}
\]

Thus, the denominator is:

\[
2.4 \times 10^{1}
\]

Now we can rewrite the entire expression:

\[
\frac{10.8 \times 10^{-7}}{2.4 \times 10^{1}}
\]

Next, divide the coefficients:

\[
\frac{10.8}{2.4} = 4.5
\]

And for the powers of ten:

\[
10^{-7} \div 10^{1} = 10^{-7 - 1} = 10^{-8}
\]

Thus, we have:

\[
4.5 \times 10^{-8}
\]

Finally, we convert this to scientific notation:

The final answer is:

\[
\mathbf{4.5 \times 10^{-8}}
\]

So the correct option is **B: \(4.5 \times 10^{-8}\)**.