Question

What is left-parenthesis 3.7 times 10 Superscript negative 8 Baseline right-parenthesis Superscript 2 Baseline expressed in scientific notation?
Answer options with 4 options
A.
1.369 times 10 Superscript negative 17 Baseline
B.
1.369 times 10 Superscript negative 16 Baseline
C.
1.369 times 10 Superscript negative 15 Baseline
D.
1.369 times 10 Superscript negative 6 Baseline

Answer 1

To calculate \((3.7 \times 10^{-8})^2\), we can use the properties of exponents:

1. Square the coefficient:
\[
(3.7)^2 = 13.69
\]

2. Square the power of ten:
\[
(10^{-8})^2 = 10^{-16}
\]

Putting these two results together, we have:
\[
(3.7 \times 10^{-8})^2 = 13.69 \times 10^{-16}
\]

Now, we need to express \(13.69\) in scientific notation:
\[
13.69 = 1.369 \times 10^1
\]

Therefore, we substitute this back:
\[
13.69 \times 10^{-16} = 1.369 \times 10^1 \times 10^{-16} = 1.369 \times 10^{-15}
\]

Thus, the final answer is:
\[
1.369 \times 10^{-15}
\]

The correct option is:
C. \(1.369 \times 10^{-15}\)