Question

Convert the following to the equivalent measures indicated. \(61 / 2 \mathrm{oz}=\) ______ \(\mathrm{mL}\)

Short answer

61/2 oz = 902.99 mL.

Step-by-step solution

Understand the Conversion Factor

To convert fluid ounces (oz) to milliliters (mL), we need to know the conversion factor. 1 fluid ounce is approximately equal to 29.5735 milliliters. This means that to convert ounces to milliliters, we multiply the number of ounces by 29.5735.

Identify the Given Quantity

The given measurement in the problem is \( \frac{61}{2} \) ounces. This represents a fraction, which we can convert to a decimal to make calculations easier.

Convert the Fraction to a Decimal

First, solve \( \frac{61}{2} \) to find its decimal form. Divide 61 by 2 to get 30.5 ounces.

Perform the Conversion Calculation

Now that we have 30.5 ounces, use the conversion factor from Step 1. Multiply 30.5 by 29.5735 to convert ounces to milliliters. Calculation: \[ 30.5 \times 29.5735 = 902.99325 \]

Round to an Appropriate Precision

Since the question does not specify the precision needed, we can round the result to two decimal places, which is common in measurements. So, 902.99325 rounds to 902.99 milliliters.

Key concepts

Conversion Factor

A conversion factor is a numerical value used to change a measurement from one unit to another. It's crucial in metric conversion problems, like going from fluid ounces to milliliters. The conversion factor is derived from the known relationship between the two units. For instance, 1 fluid ounce is equivalent to approximately 29.5735 milliliters.

Understanding conversion factors helps us seamlessly translate between units by simply multiplying the original measurement by this factor. These factors act as bridges across different measurement systems, allowing accurate conversions in a standardized way. Mastering them is crucial for any student tackling metric conversion problems.

Fluid Ounces to Milliliters

When converting fluid ounces to milliliters, we apply the conversion factor directly to the given amount. In this case, we deal with fluid ounces and know that each ounce equals roughly 29.5735 milliliters.

Here's how the conversion process works:

• Start with the number of fluid ounces you need to convert, which might be in a fraction or decimal form.
• Use the conversion factor: multiply the number of fluid ounces by 29.5735.
• This product will give you the equivalent measurement in milliliters.

For our specific problem, converting 30.5 fluid ounces—obtained after simplifying the fraction \(61/2\)—to milliliters involves multiplication, yielding the final result of approximately 902.99 milliliters.

Measurement Precision

Precision in measurement describes how detailed a number is. It's all about the number of decimal places used when reporting the result. While converting fluid ounces to milliliters, precision ensures the accuracy of your calculation. Some contexts require high precision, while others allow more flexibility.

After computing the conversion, it's often necessary to round the result. If the problem does not specify, a common practice is rounding to two decimal places. This level of precision balances the need for accuracy with clarity, making the number easier to work with in further calculations or comparisons.

For this exercise, we started with 902.99325 milliliters, eventually rounding it to 902.99 milliliters. This approach maintains accuracy while keeping the number manageable.

Arithmetic Operations

Arithmetic operations form the backbone of metric conversions. Multiplication, division, addition, and subtraction are tools we use to manipulate numbers and quantities. For converting units like fluid ounces to milliliters, multiplication is key.

Here’s a breakdown of the steps using arithmetic:

• Identify the given fraction or number. In our problem, it was \(rac{61}{2}\) ounces.
• Simplify if needed, using division to convert fractions to decimals (61 divided by 2 equals 30.5).
• Apply the conversion factor using multiplication: multiply 30.5 by 29.5735 to get the milliliter equivalent.
• Finally, use rounding as necessary to ensure precision.

Building proficiency in these operations helps solve various conversion problems efficiently and accurately.