Solve each of the following problems using one or more conversion factors:
a. A container holds 0.500 qt of liquid. How many milliliters of lemonade will it hold?

Verified step by step guidance

1. Step 1: Identify the given quantity and the desired unit. The given quantity is 0.500 qt (quarts), and the desired unit is milliliters (mL).
2. Step 2: Determine the conversion factors needed. First, convert quarts to liters using the conversion factor: 1 qt = 0.946 L. Then, convert liters to milliliters using the conversion factor: 1 L = 1000 mL.
3. Step 3: Set up the conversion using dimensional analysis. Multiply the given quantity (0.500 qt) by the first conversion factor (0.946 L/1 qt) to convert quarts to liters.
4. Step 4: Take the result from Step 3 and multiply it by the second conversion factor (1000 mL/1 L) to convert liters to milliliters.
5. Step 5: Ensure that all units cancel appropriately, leaving only milliliters as the final unit. The calculation will yield the number of milliliters of lemonade the container can hold.

Key Concepts

Conversion Factors

Conversion factors are ratios that express how many of one unit are equal to another unit. They are essential in dimensional analysis, allowing for the conversion of measurements from one system to another, such as from quarts to milliliters. For example, knowing that 1 quart is approximately 946.35 milliliters enables the calculation of volume in different units.

Volume Measurement

Volume measurement refers to the quantification of three-dimensional space occupied by a substance. Common units of volume include liters, milliliters, quarts, and gallons. Understanding the relationship between these units is crucial for solving problems that involve liquid capacities, such as converting quarts to milliliters in this scenario.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert one set of units to another by multiplying by appropriate conversion factors. This method ensures that units cancel appropriately, leading to the desired unit in the final answer. It is a systematic approach that helps verify the correctness of calculations involving different measurement systems.