Step 1 :Translate the problem into a mathematical equation. Let's denote the volume of 10 drops as x. Then we can set up the proportion as follows: \(\frac{10000 \text{ drops}}{100 \text{ fluid ounces}} = \frac{10 \text{ drops}}{x \text{ fluid ounces}}\)
Step 2 :Solve the equation for x. Cross multiply to get \(10000 \times x = 100 \times 10\)
Step 3 :Simplify the equation to get \(x = \frac{100 \times 10}{10000}\)
Step 4 :Calculate the value of x to get \(x = 0.1\)
Step 5 :Final Answer: The volume of 10 drops is \(\boxed{0.1}\) fluid ounces.