8. Azelastine hydrochloride is an antihistamine nasal spray. A standard-size container holds one fluid ounce (oz) of the liquid. You are searching for this medication at a chemist's and are asked how many millilitres (mL) there are in one fluid ounce. Using the following conversion factors, determine the number of millilitres in a volume of one fluid ounce: 1 gallon (gal) = 128 oz, 3.785 x 10 cubic metres (m ^ 3) = 1 gal, and 1mL = 10 ^ - 6 * m ^ 3

To solve this problem, we'll use the provided conversion factors step by step. We need to convert 1 fluid ounce (oz) into milliliters (mL). Here are the steps:

### Given Conversion Factors:
1. \(1 \text{ gallon (gal)} = 128 \text{ oz}\)
2. \(3.785 \times 10^{-3} \text{ cubic meters (m}^3) = 1 \text{ gallon (gal)}\)
3. \(1 \text{ mL} = 10^{-6} \text{ cubic meters (m}^3)\)

### Step-by-Step Conversion:

1. **Convert ounces to gallons:**

   Since 1 gallon = 128 oz,
   \[
   1 \text{ oz} = \frac{1}{128} \text{ gal}
   \]

2. **Convert gallons to cubic meters:**

   Since \(1 \text{ gal} = 3.785 \times 10^{-3} \text{ m}^3\),
   \[
   1 \text{ oz} = \frac{1}{128} \times 3.785 \times 10^{-3} \text{ m}^3
   \]

   Simplifying this:
   \[
   1 \text{ oz} = \frac{3.785 \times 10^{-3}}{128} \text{ m}^3
   \]

   Calculating the value:
   \[
   1 \text{ oz} \approx 2.95703125 \times 10^{-5} \text{ m}^3
   \]

3. **Convert cubic meters to milliliters:**

   Since \(1 \text{ mL} = 10^{-6} \text{ m}^3\),
   \[
   1 \text{ oz} = \frac{2.95703125 \times 10^{-5}}{10^{-6}} \text{ mL}
   \]
   \[
   1 \text{ oz} \approx 29.57 \text{ mL}
   \]

### Conclusion:
There are approximately **29.57 milliliters (mL)** in one fluid ounce (oz).

Would you like more details, or do you have any questions?

### Related Questions:
1. How would you convert milliliters to ounces?
2. If a container holds 50 mL, how many fluid ounces is that?
3. What is the conversion factor between cubic inches and cubic meters?
4. How many fluid ounces are there in a gallon?
5. What is the volume in cubic centimeters for one fluid ounce?

### Tip:
When converting units, it's helpful to work through the problem step-by-step, ensuring each conversion factor is applied correctly. This reduces the chance of making errors in complex calculations.

Learn how to convert fluid ounces to milliliters using the given conversion factors step-by-step. This problem covers unit conversion and metric system concepts, including volume conversion. Suitable for high school students.

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