Question

Complete the following


(3.2 x 10^4) (8.03 x 10 ^-8)

Image reference
A.
25.696 x 10^ -4

B.
2.5696 x 10^4

C.
2.5696 x 10^-3

D.
25.696 x 10^3

Answer 1

To solve \((3.2 \times 10^4) \cdot (8.03 \times 10^{-8})\), we can first multiply the coefficients (3.2 and 8.03) and then add the exponents of 10.

1. Multiply the coefficients:
\[
3.2 \times 8.03 = 25.6896
\]

2. Add the exponents:
\[
10^4 \times 10^{-8} = 10^{4 + (-8)} = 10^{-4}
\]

3. Combine the results:
\[
25.6896 \times 10^{-4}
\]

Now, we can express it in scientific notation. To convert \(25.6896\) to scientific notation, we rewrite it as:
\[
2.56896 \times 10^1
\]
Thus,
\[
25.6896 \times 10^{-4} = 2.56896 \times 10^{1} \times 10^{-4} = 2.56896 \times 10^{-3}
\]

So, rounded to four significant figures, we get:
\[
2.5696 \times 10^{-3}
\]

The correct answer is:
**C. \(2.5696 \times 10^{-3}\)**.