Question

Convert the following to the equivalent measures indicated. $4\frac{1}{2}\mathrm{pt}=$ ______ $\mathrm{mL}$

Short answer

2129.292 mL

Step-by-step solution

Understand the Unit Conversion

First, identify the conversion factor between pints and milliliters. In the metric system, 1 US pint is equivalent to approximately 473.176 milliliters. Therefore, our goal is to convert the given pints into milliliters using this conversion rate.

Convert the Mixed Number to an Improper Fraction

The given quantity is a mixed number: $4\frac{1}{2}$. Convert it to an improper fraction to make calculations easier:$$4\frac{1}{2}=\frac{4\times 2+1}{2}=\frac{9}{2}$$

Perform the Conversion

Now that we have the pints as an improper fraction, multiply by the conversion factor to find the equivalent in milliliters:$$\frac{9}{2}\text{ pints}\times 473.176\text{ mL/pint}=\frac{9\times 473.176}{2}\text{ mL}$$

Calculate the Result

Carry out the multiplication and division to get the milliliters:$$\frac{9\times 473.176}{2}=2129.292\text{ mL}$$

State the Final Answer

The equivalent volume of $4\frac{1}{2}$ pints in milliliters is 2129.292 mL.

Key concepts

Metric System

The metric system is an international decimalized system of measurement, which is easy to understand due to its use of base ten. It's widely used around the world, except for a few countries like the United States, which primarily uses the imperial system. The metric system's simplicity arises from its uniform conversion rates, such as 1 meter is 100 centimeters, making calculations straightforward.

In the metric system, volume is typically measured in liters and milliliters. Knowing key conversions is essential. For example, 1 liter equals 1000 milliliters. Understanding these conversions helps you shift seamlessly between different units of volume within the metric system.

Improper Fractions

Improper fractions are fractions where the numerator is greater than or equal to the denominator. They often come into play when dealing with mixed numbers to simplify calculations.

To convert a mixed number, such as $4\frac{1}{2}$, to an improper fraction, multiply the whole number by the denominator and add the numerator. This converts it to a fraction entirely greater than one. For instance, $4\times 2+1=9$, so $4\frac{1}{2}=\frac{9}{2}$. Improper fractions allow for easier multiplication and division, as seen in measurement conversions.

Measurement Conversion

Measurement conversion involves changing a measurement from one unit to another, using a specific conversion factor. This is crucial both in everyday tasks and more specialized areas like scientific measurements.

When converting between measurement systems, such as the metric and imperial systems, finding the correct conversion factor is vital. In our example, converting pints to milliliters, we use the factor of 1 pint equals roughly 473.176 milliliters. Once the conversion factor is identified, multiply the measurement's proper value by this factor to obtain the equivalent in the desired unit.

Volume Conversion

Volume conversion is the process of changing the volume of a liquid or gas to another unit, often using different systems such as from pints in the imperial system to milliliters in the metric system.

To perform a volume conversion effectively, first ensure accurate use of the computational steps. Convert mixed numbers to improper fractions, apply the conversion factor accurately, and perform multiplication and division carefully. Thus, converting $4\frac{1}{2}$ pints to milliliters involves multiplying $\frac{9}{2}$ by 473.176, yielding 2129.292 mL. Accurate volume conversion is vital in fields ranging from cooking to industrial applications.