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 negative cube m³

To determine how many milliliters (mL) there are in one fluid ounce (oz), we can use the provided conversion factors. Let's go through the calculations step by step:

### Step 1: Convert fluid ounces to gallons
Given:
- 1 gallon (gal) = 128 oz

Thus, the number of gallons in 1 fluid ounce is:
\[
\text{Volume in gallons} = \frac{1 \, \text{oz}}{128 \, \text{oz/gal}} = \frac{1}{128} \, \text{gal}
\]

### Step 2: Convert gallons to cubic meters
Given:
- \( 1 \, \text{gal} = 3.785 \times 10^{-3} \, \text{m}^3 \)

Now, convert the volume in gallons to cubic meters:
\[
\text{Volume in cubic meters} = \frac{1}{128} \, \text{gal} \times 3.785 \times 10^{-3} \, \text{m}^3/\text{gal} = \frac{3.785 \times 10^{-3}}{128} \, \text{m}^3
\]

### Step 3: Convert cubic meters to milliliters
Given:
- \( 1 \, \text{mL} = 10^{-6} \, \text{m}^3 \)

So, the number of milliliters in the calculated cubic meters:
\[
\text{Volume in mL} = \frac{3.785 \times 10^{-3}}{128} \, \text{m}^3 \times \frac{1 \, \text{mL}}{10^{-6} \, \text{m}^3}
\]

Simplify the equation:
\[
\text{Volume in mL} = \frac{3.785 \times 10^{-3}}{128} \times 10^6 \, \text{mL}
\]

Calculate the value:
\[
\text{Volume in mL} = \frac{3.785 \times 10^3}{128} \, \text{mL} \approx 29.57 \, \text{mL}
\]

### Final Answer
There are approximately **29.57 milliliters** in one fluid ounce.

Would you like more details on this conversion or have any questions?

Here are five related questions to expand on this topic:
1. How would you convert 500 mL to fluid ounces using the same conversion factors?
2. What is the volume of 2 gallons in milliliters?
3. How many cubic centimeters (cm³) are there in one fluid ounce?
4. Can you determine the number of fluid ounces in a liter?
5. How would the conversion change if you were converting imperial fluid ounces instead?

**Tip:** When working with conversions, always ensure that your units cancel appropriately to end up with the correct units in your final answer.

Learn how to convert fluid ounces to milliliters using conversion factors. This detailed guide covers unit conversions from fluid ounces to gallons, gallons to cubic meters, and cubic meters to milliliters. Discover the calculation steps and key formulas involved.

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