Question

Set up the problem using dimensional analysis and make the conversion as indicated. $3\mathrm{qt}=$ ______ $\mathrm{mL}$

Short answer

3 quarts is equivalent to 2839.059 mL.

Step-by-step solution

Understand the Problem

We need to convert 3 quarts (qt) into milliliters (mL). To do this, we'll use dimensional analysis which involves using conversion factors to change from one unit to another.

Identify Conversion Factors

A common conversion factor is 1 quart (qt) = 946.353 milliliters (mL). We will use this conversion factor to perform the conversion from quarts to milliliters.

Set Up the Dimensional Analysis

Start with the given quantity, 3 qt. Multiply it by the conversion factor to cancel out quarts and convert to milliliters:$$3\text{ qt}\times \frac{946.353\text{ mL}}{1\text{ qt}}$$

Perform the Multiplication

Multiply 3 by 946.353 to find the equivalent volume in milliliters:$$3\times 946.353=2839.059$$

Interpret the Results

After performing the multiplication, the conversion is complete. Thus, 3 quarts is equivalent to 2839.059 milliliters.

Key concepts

Unit Conversion

Unit conversion is an essential skill in solving various mathematical and scientific problems. It involves changing a measurement from one unit to another while maintaining the same value. For example, if we're given a volume in quarts and need to express it in milliliters, we perform a unit conversion.

Understanding the relationship between these units is crucial. In this case, the relationship is 1 quart equals 946.353 milliliters. This is known as a conversion factor.

Conversion factors are ratios that express the same quantity in different units. They are used to multiply or divide to perform the conversion.

The key to successful unit conversion is setting up the problem correctly. This often involves writing the units as fractions and ensuring that unwanted units cancel out, leaving you with the desired units. This process ensures precision and accuracy in calculations.

Volume Measurement

Volume measurement refers to quantifying the amount of space an object or substance occupies. Common units of volume in the metric system include milliliters (mL), liters (L), and cubic meters (m³). In the U.S. customary system, common volume units include quarts, pints, and gallons.

When measuring volume, using dimensional analysis helps compare and convert these different units systematically.

Milliliters are often used for small quantities, making them ideal for liquids. Quarts are commonly used in culinary settings in the United States.

Understanding these units and how to convert between them is crucial. It helps in many fields, including cooking, chemistry, and engineering. Converting 3 quarts to milliliters allows you to express the measurement in a more universally understood unit like the milliliter, useful in science and medicine.

Mathematical Problem-Solving

Mathematical problem-solving involves using a step-by-step approach to address questions or calculations. This methodology is useful in unit conversion exercises like converting quarts to milliliters.

The first step is always understanding the problem. You need to know what you are converting and why. Following this, identify the appropriate conversion factors that will allow you to change from one unit to another.

Always multiply by the conversion factor that allows for the cancelation of the original unit. Ensure calculations are accurate by double-checking your multiplication or division steps.

Finally, interpret your results in context. This means understanding what your final calculation tells you in the real-world scenario you are dealing with. In our problem, understanding that 3 quarts is the same as 2839.059 milliliters allows for accurate measurement and application in practical situations.