Problem 33 - Introductory Chemistry Atoms First

Question

How many milliliters are there in \(246.7 \mathrm{~cm}^{3} ?\)

Step-by-Step Solution

Answer

There are \(246.7 \: \mathrm{mL}\) in \(246.7 \: \mathrm{cm}^3\).

Step 1: Know the conversion factor between cm³ and mL

Remember that 1 cm³ is equal to 1 mL.

Step 2: Write the given volume in cm³

The volume given is \(246.7 \: \mathrm{cm}^3\).

Step 3: Convert the volume from cm³ to mL

Since 1 cm³ is equal to 1 mL, the volume can be directly written as: \(246.7 \: \mathrm{cm}^3 = 246.7 \: \mathrm{mL}\)

Step 4: State the final answer

There are \(246.7 \: \mathrm{mL}\) in \(246.7 \: \mathrm{cm}^3\).

Key Concepts

Volume Conversion

Volume conversion is the process of changing the measurement of a volume from one unit to another. It is a common practice in both everyday life and scientific applications, especially when dealing with different measurement systems or units.
Understanding how to switch between different units of volume is crucial for accurately comparing or converting measurements. Here are some key points to consider:

• Make sure you know the relationship between the units involved. For example, 1 liter is equivalent to 1,000 milliliters.
• Use a consistent methodology: To convert from one unit to another, multiply or divide by the appropriate conversion factor.
• Volume can be measured in different systems, like Imperial or Metric, so it's essential to know which system you're working with.

Always double-check your calculations to avoid errors.

Cubic Centimeters to Milliliters

The conversion between cubic centimeters (\( ext{cm}^3\)) and milliliters (mL) is remarkably simple because they are equivalent. This means that 1 cubic centimeter is exactly equal to 1 milliliter. This simplicity arises because both units are part of the metric system and are designed to be interchangeable.
Here's what you should know about this conversion:

• You can directly substitute the unit \( ext{cm}^3\) with mL without any need for computation.
• This 1:1 ratio simplifies calculations in laboratory, cooking, and various practical applications.
• Understanding this equivalency is fundamental when performing volume measurements and conversions in the metric system.

Thus, converting from cubic centimeters to milliliters is one of the easiest conversions you can encounter.

Metric System Conversion

The metric system is an internationally agreed decimal system of measurement. It's based on multiples of ten, which makes conversions straightforward and calculations easier. Within this system, units of volume include liters, milliliters, and cubic centimeters, among others.
Here are some important aspects of metric system conversions:

• Metric conversions are simplified when you remember key equivalencies, such as 1,000 milliliters equals 1 liter, or 1 cubic meter equals 1,000 liters.
• The main advantage of the metric system is its universality and ease of understanding due to its decimal nature.
• When converting in the metric system, it often only requires moving the decimal point, which minimizes errors and speeds up the computation process.

The metric system's simplicity makes it exceptionally practical for scientific, academic, and day-to-day activities worldwide.