Question

The volume 0.250 L could also be expressed as _____ mL.

Short answer

The volume 0.250 L could also be expressed as \(250\) mL.

Step-by-step solution

Identify the given volume and conversion factor

We are given a volume of 0.250 L which we need to convert to mL. The conversion factor is 1 liter = 1000 milliliters.

Set up the conversion equation

To convert the volume in liters to milliliters, we can set up a proportion equation using the conversion factor. Volume (mL) = (Volume in L) × (1000 mL/1 L)

Substitute the given volume and solve for the volume in mL

Now, substitute the given volume (0.250 L) into the equation and solve for the volume in mL: Volume (mL) = (0.250 L) × (1000 mL/1 L)

Perform the calculation

Now we perform the calculation: Volume (mL) = 0.250 × 1000

Write the final answer

After performing the calculation, we get the final answer: Volume (mL) = 250 mL So, the volume of 0.250 L could also be expressed as 250 mL.

Key concepts

Liters to Milliliters

When working with volume, understanding how to convert between different units is essential. Liters and milliliters are two commonly used units, where a liter represents a larger volume and a milliliter represents a smaller volume. The key to converting from liters to milliliters is knowing that one liter is equivalent to one thousand milliliters. This relationship simplifies conversions considerably.

For instance, to convert a volume given in liters to milliliters, simply multiply the number of liters by 1000. If you have a volume of 0.250 liters, you can easily determine the corresponding volume in milliliters by calculating \(0.250 \times 1000 = 250\) milliliters. This straightforward multiplication allows for quick conversions and is a useful tool in various applications, from cooking to science experiments.

Conversion Factors

Conversion factors are the bread and butter of unit conversions. They are mathematical tools that allow you to convert a measurement in one unit to an equivalent measurement in another unit. A conversion factor is a ratio that expresses how many of one unit are equal to another.

For example, the conversion factor for converting liters to milliliters is \(1000 \text{ mL}/1 \text{ L}\), because there are 1000 milliliters in one liter. When you multiply a measurement by a conversion factor, the original unit is canceled out, and the new unit takes its place. It's important to line up the units so that they cancel properly, ensuring that the factor is set as \(\text{unit you want})/(\text{unit you have}\). By consistently employing conversion factors, you'll make error-free conversions between units.

Dimensional Analysis

Dimensional analysis, also known as the factor-label method, is a technique widely used in science and engineering to convert one set of units to another. This method involves the use of conversion factors and the principle that units can be treated as algebraic quantities that can cancel each other out. When using dimensional analysis, you ensure that the final units are those desired for the answer by arranging the conversion factors in such a way that undesired units cancel out.

To perform dimensional analysis, you:

• Write down the quantity you wish to convert.
• Write down the relevant conversion factors, checking that they are properly oriented to cancel the units properly.
• Multiply the original quantity by the conversion factors and do the math.

By following this method, you guarantee that your conversion respects the relationship between units, thus providing an accurate and reliable result. Using the earlier exercise as an example, we start with \(0.250 \text{ L}\) and want to end up with milliliters. Our conversion factor is \(1000 \text{ mL}/1 \text{ L}\), so we set it up as \(0.250 \text{ L} \times 1000 \text{ mL}/1 \text{ L}\). The liter units cancel, leaving us with \(250\text{ mL}\), the converted volume.