Question

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

Short answer

$1\frac{1}{2}$ quarts is approximately 1419.5 mL.

Step-by-step solution

Convert Mixed Fraction to Improper Fraction

The given quantity is $1\frac{1}{2}$ quarts. First, convert this mixed fraction to an improper fraction. Multiply the whole number $1$ by the denominator $2$ and add the numerator $1$:$$1\cdot 2+1=3$$So, $1\frac{1}{2}=\frac{3}{2}$ quarts.

Use the Conversion Factor

Now, convert quarts to milliliters using the conversion factor: $1\text{ quart}=946.353\text{ milliliters}$. Multiply the fraction by this conversion factor:$$\frac{3}{2}\text{ qt}\times 946.353\text{ mL/qt}$$

Multiply and Simplify

Perform the multiplication to find the equivalent in milliliters:$$\frac{3}{2}\times 946.353=\frac{3\times 946.353}{2}=\frac{2839.059}{2}=1419.5295\text{ mL}$$

Round to Appropriate Precision

Since we are dealing with a standard conversion and usual precision, round the result to one decimal place:$$1419.5295\approx 1419.5\text{ mL}$$

Key concepts

Mixed Fraction

A mixed fraction is a combination of a whole number and a fraction. For example, in the fraction $1\frac{1}{2}$, $1$ is the whole number and $\frac{1}{2}$ is the fraction part. To work with mixed fractions in mathematical operations, it's often easier to first convert them into an improper fraction.

This is done by multiplying the whole number by the fraction's denominator and then adding the numerator. For instance, in our example, you multiply $1$ by $2$ and add $1$, resulting in $3$. Thus, $1\frac{1}{2}$ becomes $\frac{3}{2}$. This conversion simplifies arithmetic operations, especially when you're dealing with multiplication or division.

Conversion Factor

A conversion factor is a number used to change one set of units to another by multiplying or dividing. It's a reliable bridge between two different measurement units. For example, in this exercise, we are converting quarts to milliliters. The conversion factor given is $1\text{ quart}=946.353\text{ milliliters}$.

Using a conversion factor involves multiplying the quantity by this factor. This kind of multiplication helps you switch from one unit to another systematically.
During such operations, remember:

• Ensure the unit you want to convert from is canceled out, so you end up with the desired unit.
• Always double-check the conversion factor to confirm its correctness.

Milliliters

When we talk about milliliters, we are discussing a standard unit of volume in the metric system. Milliliters are often used for measuring liquids and are equivalent to one-thousandth of a liter. This makes them quite handy for smaller volumes, such as beverages or liquids used in laboratory settings.

In this exercise, after converting quarts to milliliters using the conversion factor, your result is a measurement expressed in milliliters.
Using milliliters in calculations offers precision as it is a smaller unit compared to liters, making it especially useful in precise measurements and scientific contexts.

Precision Rounding

Precision rounding is about adjusting a number to a specified degree of accuracy. It is essential especially when dealing with measurements, as it helps ensure results are practical and meaningful.

Rounding often requires you to consider the context or standards for the problem. In this scenario, the result of $1419.5295\text{ mL}$ from our conversion was rounded. By looking at the fifth digit after the decimal, we decided to round to the nearest tenth, resulting in $1419.5\text{ mL}$.
Remember:

• If the digit next to the last considered is 5 or more, round up.
• If it’s less than 5, round down by leaving the last considered digit unchanged.

This assures that the answer is not only precise but also suitable for most real-world situations.