To determine the scientific notation for the number 0.008005, we should follow a step-by-step process. Scientific notation typically expresses a number as a product of a coefficient between 1 and 10 and a power of 10.
### Step-by-Step Solution:
1. Identify the Coefficient:
First, we need to find a coefficient that is between 1 and 10 for our given number 0.008005. We do this by moving the decimal point to the right until we get a number between 1 and 10.
[tex]\[
0.008005 \rightarrow 8.005
\][/tex]
2. Determine the Power of 10:
Count how many places we moved the decimal point to the right. In this case, we moved the decimal point 3 places to the right:
[tex]\[
0.008005 \rightarrow \underline{8.005} \times 10^{-3}
\][/tex]
The negative sign in the exponent indicates that the original number is smaller than 1, and we moved the decimal point 3 places to the right.
3. Write in Scientific Notation:
Combining the coefficient and the power of 10, the number 0.008005 written in scientific notation is:
[tex]\[
8.005 \times 10^{-3}
\][/tex]
4. Select the Correct Option:
From the given options:
- A. [tex]\(8.500 \times 10^{-3}\)[/tex]
- B. [tex]\(8.005 \times 10^{-4}\)[/tex]
- C. [tex]\(8.005 \times 10^{-3}\)[/tex]
- D. [tex]\(8.005 \times 10^{-2}\)[/tex]
The correct answer is:
[tex]\[
\boxed{C. \, 8.005 \times 10^{-3}}
\][/tex]
Thus, the number 0.008005 written in scientific notation is [tex]\(8.005 \times 10^{-3}\)[/tex].
