Question

Set up the problem using dimensional analysis and make the conversion as indicated. \(2,400 \mathrm{~mL}=\) ______ \(\mathbf{L}\)

Short answer

2,400 mL is 2.4 L.

Step-by-step solution

Identify the Given Quantity

The given quantity is 2,400 milliliters (mL). We are required to convert this value to liters (L).

Determine Conversion Factor

Recall that the metric system conversion between milliliters and liters is based on the fact that 1 liter (L) is equivalent to 1,000 milliliters (mL). Thus, our conversion factor will be \(\frac{1 \text{ L}}{1000 \text{ mL}}\).

Set Up Dimensional Analysis Equation

We begin by writing the given unit and multiplying by the conversion factor, keeping track of units to ensure they cancel out properly. \[2,400 \text{ mL} \times \frac{1 \text{ L}}{1,000 \text{ mL}}\]

Perform the Calculation

Cancel out the mL units, so the equation becomes:\[2,400 \times \frac{1}{1,000} \text{ L} = 2.4 \text{ L}\].Thus, the calculation gives us a result of 2.4 liters.

Write the Final Result

Therefore, 2,400 mL is equivalent to 2.4 L when converted using dimensional analysis.

Key concepts

Metric System Conversion

The metric system is a decimal system of measurement used globally for scientific and everyday purposes . It is based on powers of ten, making conversions straightforward and consistent. Understanding metric system conversion is crucial, especially when working with different measurements like length, mass, and volume.
One of the key aspects is remembering the base units and their multiples or sub-multiples. For volume, the base unit is liters. Conversions are made easy because they usually involve just shifting the decimal point. For instance, converting between liters and milliliters requires moving the decimal point three places.

• 1 liter (L) = 1,000 milliliters (mL)
• 1 milliliter (mL) = 0.001 liters (L)

Familiarity with these conversions is essential for dimensional analysis.

Liters and Milliliters

When dealing with liquid volumes in the metric system, liters and milliliters are the most common units. A liter is a standard unit for larger volumes of liquid, such as a bottle of water or a carton of juice. On the other hand, milliliters measure smaller quantities, such as a tablespoon of medicine or the amount in a small perfume vial.
Understanding the relationship between these two units is simple with the metric base-10 system. Each liter is divided into 1,000 milliliters. This direct relationship makes conversions easy.
When confronted with a task like converting milliliters to liters:

• You know there are 1,000 milliliters in every liter.
• You divide the milliliters by 1,000 to get the result in liters.

For example, converting 2,400 milliliters to liters requires dividing 2,400 by 1,000, resulting in 2.4 liters. This clarity ensures you understand the process and results.

Conversion Factor

A conversion factor is a powerful tool in dimensional analysis, providing a bridge between different units of measurement. It is essentially a fraction or ratio that allows you to convert one unit to another without changing the quantity's original value.
Selecting the correct conversion factor is vital for a successful conversion. For example, when converting milliliters to liters, the conversion factor is 1 liter per 1,000 milliliters.

• The conversion factor used in an equation ensures units cancel out correctly.
• This systematic cancellation of units ensures that you're left with the desired unit - in this case, liters.

In practice, you multiply the number of milliliters by the conversion factor. For instance, multiplying 2,400 mL by \( \frac{1 \text{ L}}{1,000 \text{ mL}} \) helps eliminate milliliters, resulting in 2.4 liters.