## Answer :

### 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].