Question

Convert 0.840 qt to milliliters in a single calculation using more than one conversion factor.

Short answer

0.840 qt is approximately 794.96 mL.

Step-by-step solution

Understand the Conversion Factors

To convert quarts to milliliters, we need two conversion factors: 1 quart is equivalent to 4 cups, and 1 cup is equivalent to 236.588 milliliters.

Convert Quarts to Cups

Since 1 quart is equal to 4 cups, we multiply the given quantity in quarts by this factor:\[0.840 \, ext{qt} \times 4 \, \frac{ ext{cups}}{ ext{qt}} = 3.36 \, ext{cups}\]

Convert Cups to Milliliters

Now convert cups to milliliters knowing 1 cup equals 236.588 mL:\[3.36 \, ext{cups} \times 236.588 \, \frac{ ext{mL}}{ ext{cup}} = 794.957 \, ext{mL}\]

Check the Calculation

Review the calculations to confirm that all unit conversions were applied correctly and that each step follows logically from the previous one.

Key concepts

Quarts to Milliliters

Converting from quarts to milliliters can seem challenging at first. It involves moving from one system of measurement (imperial) to another (metric). Specifically, the task is to convert a volume measured in quarts, which is commonly used in the United States, to milliliters, which is a metric unit of volume used worldwide. A quart is slightly less than a liter as it roughly equals 946.353 milliliters. However, the conversion process can be broken into smaller, manageable steps, utilizing intermediary units such as cups that bridge the gap between quarts and milliliters.

By understanding the relationship between these units, you can simplify the conversion process and minimize errors. This process often involves using multiple conversion factors to gradually convert from one unit to another. In our case, converting quarts to cups and then cups to milliliters provided a clear pathway to solve the problem in an organized manner.

Conversion Factors

A conversion factor is a ratio that expresses how many of one unit is equivalent to another. They are crucial in converting from one measurement system to another, such as quarts to milliliters. In the exercise, two conversion factors were used:

• 1 quart = 4 cups
• 1 cup = 236.588 milliliters

These conversion factors link the imperial and metric systems by translating quarts into cups, and then cups into milliliters.

It's important to set up conversion factors correctly. For instance, when converting quarts to cups, you multiply by the factor \(4 \, \frac{cups}{qt}\). This setup ensures that the quarts unit cancels out, leaving you with cups. By multiplying 3.36 cups by \(236.588 \, \frac{mL}{cup}\), you again cancel out cups to find the answer in milliliters. Always double-check the units to make sure they cancel properly and guide you to the desired units.

Measurement Conversion

Measurement conversion is the process of converting one unit of measure to another. It is an essential skill across many fields, including science, engineering, and cooking. In our case of converting quarts to milliliters, understanding the principle of measurement conversion is crucial.

Every measurement conversion involves a conversion factor. This factor acts as a bridge from one unit to another, affirming the importance of knowing various conversions. It helps in accurate measurement, which is vital in real-life applications. Ultimately, each conversion factor paves the way for precise and reliable conversions, ensuring the integrity and uniformity of data across diverse domains.

Volume Conversion

Volume conversion is specifically about changing the unit of volume from one system to another. Whether you're dealing with ounces, liters, gallons, or cups, understanding volume conversion is key to correctly interpreting and comparing different measurements.

Quarts and milliliters both measure liquid volume but belong to different measurement systems. Knowing how these units interrelate is necessary for problems involving international recipes or scientific experiments where precise volume measurement is required. Volume conversion processes, like the one described in the exercise, help create consistency across varying standards, making it easier to understand quantities in a global context.