Question

Given that \(1 \mathrm{L}=1000 \mathrm{mL},\) determine what conversion factor is appropriate to convert 2.75 L to milliliters; to convert 255 mL to liters.

Short answer

The appropriate conversion factors are 1000 mL/L for converting 2.75 L to milliliters and 0.001 L/mL for converting 255 mL to liters. Using these factors, we find that 2.75 L is equal to 2750 mL and 255 mL is equal to 0.255 L.

Step-by-step solution

Write the conversion factors with the correct units

We need two conversion factors - one to convert from Liters to milliliters and another one to convert from milliliters to Liters. 1 L = 1000 mL   (Conversion factor 1) 1 mL = 0.001 L   (Conversion factor 2) These conversion factors can be obtained by dividing both sides of the first conversion factor by 1000.

Convert 2.75 L to milliliters

To convert 2.75 L to milliliters, we will use Conversion factor 1 (1 L = 1000 mL). We will multiply the liters by the conversion factor to get the milliliters. 2.75 L × 1000 mL/L = 2750 mL Here, the unit 'L' gets canceled out, and we are left with the unit 'mL'. So, 2.75 L is equal to 2750 mL.

Convert 255 mL to liters

To convert 255 mL to liters, we will use Conversion factor 2 (1 mL = 0.001 L). We will multiply the milliliters by the conversion factor to get the liters. 255 mL × 0.001 L/mL = 0.255 L Here, the unit 'mL' gets canceled out, and we are left with the unit 'L'. So, 255 mL is equal to 0.255 L. The conversion factors to convert 2.75 L to milliliters and 255 mL to liters are 1000 mL/L and 0.001 L/mL, respectively.

Key concepts

Liters to Milliliters Conversion

Converting liters to milliliters is a straightforward process. The key lies in understanding that the metric system is based on multiples of ten, making calculations relatively easy. The conversion factor for liters to milliliters is

• 1 liter
• = 1000 milliliters

To convert, you simply multiply the number of liters by 1000.
For example, if you have 2.75 liters, you multiply \[2.75 \times 1000 = 2750\] milliliters.
When you perform this multiplication, you cancel out the 'liter' unit and are left with milliliters.Understanding this connection between units helps you grasp how large one unit is compared to another. A liter is a larger unit than a milliliter, so there are many milliliters in just one liter. This core concept of unit size difference is foundational to making conversions within the metric system.

Milliliters to Liters Conversion

Converting milliliters to liters involves reversing the process used for converting liters to milliliters. Here, the goal is to determine how many liters a certain amount of milliliters corresponds to. The essential conversion factor here is:

• 1 milliliter
• = 0.001 liters

To perform the conversion, you multiply the number of milliliters by 0.001.
For instance, converting 255 milliliters to liters involves the calculation \[255 \times 0.001 = 0.255\] liters.
By multiplying by 0.001, the 'milliliter' unit cancels out, and you're left with 'liters'. This is possible because you're essentially scaling down the quantity by the conversion factor. This conversion is a great example of scaling in the metric system, allowing you to precisely move between quantities, reflecting the reduced size of each milliliter in comparison to a liter.

Metric System Conversions

The metric system is a universally adopted decimal-based system used for measurements. Its simplicity comes from the fact that it is based on powers of ten which facilitates easy conversions between units. This system is predominantly used globally because it standardizes units and makes calculations simpler. For converting between units in the metric system, you simply need to know the conversion factor, which is a value you multiply or divide by to convert from one unit to another. In the examples provided:

• Liters to milliliters: Multiply by 1000.
• Milliliters to liters: Multiply by 0.001.

These conversion factors are derived from the fact that larger units contain smaller units, with each larger unit typically being ten times greater in magnitude than the unit immediately below it. This pattern holds true across the board in the metric system, making it reliable and easy for scientists, educators, and students across various fields. By mastering these basic conversion techniques, you can effortlessly switch between different metric units, be it for classroom exercises or practical situations in daily life.