Question

Set up the problem using dimensional analysis and make the conversion as indicated. \(125 \mathrm{~mL}=\) ______ \(\mathrm{L}\)

Short answer

125 mL is 0.125 L.

Step-by-step solution

Identify the Conversion Factor

In this step, we figure out the conversion factor between milliliters and liters. The conversion is based on the fact that there are 1000 milliliters in one liter. Thus, the conversion factor is \(1 \text{ L} = 1000 \text{ mL}\).

Set Up the Problem Using Dimensional Analysis

To use dimensional analysis, start by writing the quantity you want to convert, in this case, \(125 \text{ mL}\), and set up a fraction that will cancel milliliters and introduce liters. The setup is: \[125 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}}\]This fraction will convert mL to L, as milliliters will cancel out.

Perform the Conversion

Perform the multiplication from the previous step:\[125 \times \frac{1}{1000} = 0.125 \]The unit that remains after canceling milliliters is liters, so the result is \(0.125 \text{ L}\).

Key concepts

Unit Conversion

Understanding unit conversion is essential in many fields such as science, engineering, and everyday activities. The basic idea is to convert a quantity expressed in one set of units to another set of units, without changing the actual amount. This is crucial for consistency and clear communication. For example, if someone gives you the quantity of any liquid in milliliters (mL) but you need it in liters (L), you must perform a unit conversion. Unit conversion requires a process called dimensional analysis. Dimensional analysis involves the use of conversion factors, which are ratios that express how many of one unit are equivalent to another. It ensures that the dimensions of the quantity are properly converted, leading to a meaningful and useful result.

Milliliters to Liters Conversion

Converting milliliters to liters is a common example of unit conversion using dimensional analysis. One liter is equivalent to 1000 milliliters. This means if you have 1000 milliliters, you have exactly one liter. Knowing this relationship, you can convert any amount in milliliters to liters by dividing the number of milliliters by 1000.Let's say we have 125 mL and we need to find out how many liters that is. Using our relationship, we set up the conversion as follows:

• Write the quantity: 125 mL
• Multiply by the conversion factor: \(\frac{1 \text{ L}}{1000 \text{ mL}}\)

This setup shows that you're dividing 125 by 1000, converting mL to L. After performing the calculation, you will find that 125 mL equals 0.125 L.

Conversion Factors

Conversion factors are essential in the process of unit conversion. They are essentially fractions that denote the equality of two different units. For instance, when converting milliliters to liters, we use the conversion factor \(1 \text{ L} = 1000 \text{ mL}\).The beauty of conversion factors is that they allow us to cancel out the unwanted units, effectively converting one unit to another. By multiplying by a fraction where the undesired unit is in the denominator, those units are canceled out, leaving us with the desired units. This is a reliable method because it conserves the quantity across conversions.For example, if you have 125 mL and use the conversion factor \(\frac{1 \text{ L}}{1000 \text{ mL}}\), the mL units cancel out, providing an answer in liters. Conversion factors thus ensure precision and accuracy in unit conversions.