Question

Convert the following amounts of fluid to milliliters. \(3 \frac{1}{2} \mathrm{oz}=\) ______ \(\mathrm{mL}\)

Short answer

3.5 oz is approximately 103.51 mL.

Step-by-step solution

Determine Conversion Factor

To convert fluid ounces (oz) to milliliters (mL), you need to know that 1 fluid ounce is approximately equal to 29.5735 milliliters.

Convert Whole Ounces to Milliliters

First, convert the whole number of ounces: 3 oz. Multiply 3 oz by the conversion factor: \[ 3 \text{ oz} \times 29.5735 \text{ mL/oz} = 88.7205 \text{ mL} \]

Convert Fractional Ounces to Milliliters

Now, convert the fractional part: \(\frac{1}{2}\) oz. Multiply \(\frac{1}{2}\) oz by the conversion factor: \[ \frac{1}{2} \text{ oz} \times 29.5735 \text{ mL/oz} = 14.78675 \text{ mL} \]

Add the Converts Quantities

Add the milliliters from the whole ounces and the fractional ounces:\[ 88.7205 \text{ mL} + 14.78675 \text{ mL} = 103.50725 \text{ mL} \]

Round the Final Answer

Round the answer to two decimal places for convenience:\[ 103.50725 \text{ mL} \approx 103.51 \text{ mL} \]

Key concepts

Conversion Factor

When converting units, one of the key concepts is the conversion factor. A conversion factor is a ratio that expresses how many of one unit are equivalent to another. It is crucial in bridge-building between different measurement systems. In this context, the conversion factor between fluid ounces and milliliters is 29.5735. This means that every fluid ounce corresponds to approximately 29.5735 milliliters.

Understanding and using the correct conversion factor ensures that our conversions are accurate. If you ever switch between different measurements, make sure to use an appropriate and accurate conversion factor. Incorrect factors can lead to significant errors, making it crucial to double-check their validity in reliable resources.

Remember, the conversion factor itself is a constant that aids in calculating equal measurements across different systems.

Unit Conversion

Unit conversion is the process of converting a measured quantity from one unit to another. This often involves multiplying the amount by the conversion factor.

Let's walk through how to efficiently conduct a unit conversion. Using the conversion factor from fluid ounces to milliliters mentioned above:

• Take the quantity in the original unit (e.g., fluid ounces).
• Multiply it by the conversion factor to achieve the unit you wish to convert to (e.g., milliliters).

This simple multiplication shifts the original unit to the desired one, making unit conversion a powerful tool in science and daily life.

In the case of both whole and fractional numbers, as demonstrated in the step-by-step solution, each part should be converted separately by the same conversion factor and then summed up to achieve a unified result.

Milliliters Calculation

Calculating in milliliters can often involve dealing with both whole numbers and fractions, especially when converting values from fluid ounces. To manage this, one can break down the task into two clear steps:

First, convert the whole number portion of ounces by multiplying it with the conversion factor. This gives the milliliter equivalent for the whole number. For instance, converting 3 ounces gives us 88.7205 mL.

Secondly, handle the fractional portion in a similar manner, ensuring the conversion maintains accuracy. For example, when converting \( \frac{1}{2} \) ounce, the resulting milliliters is 14.78675 mL.

Finally, add the two converted amounts together to achieve the total milliliters from ounces. Don't forget to round your final answer, often to two decimal places, for a neat and clear result, like our final approximation of 103.51 mL. Rounding ensures a more digestible and practical number, especially in real-life applications.