Problem 79 - Chemistry Principles and Practice

Question

Wine sold in Europe has its volume labeled in centiliters (cL). If wine is sold in 750 -mL bottles, how many centiliters is this?

Step-by-Step Solution

Answer

750 mL is 75 cL.

Step 1: Understanding Milliliters to Centiliters Conversion

One centiliter (cL) is equal to 10 milliliters (mL). To convert milliliters to centiliters, we need to divide the number of milliliters by 10. This is because each centiliter contains 10 milliliters.

Step 2: Setting Up the Conversion

We start with 750 milliliters (mL). According to the conversion rule, we will use the formula: \[ ext{centiliters} = rac{ ext{milliliters}}{10}\]So, we'll substitute 750 mL for milliliters in the conversion formula.

Step 3: Performing the Conversion

Replacing 750 mL in the formula gives us:\[ ext{centiliters} = rac{750}{10}\]Divide 750 by 10 to convert milliliters to centiliters.

Step 4: Calculating the Result

After dividing, we find:\[ ext{centiliters} = 75\]Therefore, 750 mL is equivalent to 75 cL.

Key Concepts

Understanding the Conversion: Milliliters to Centiliters

The conversion from milliliters to centiliters is a basic but essential part of understanding volume measurements in the metric system. When working with liquid volumes, it's common to switch between these units. A milliliter (mL) is a unit of volume that is equal to one thousandth of a liter, while a centiliter (cL) is equal to one hundredth of a liter. This means that

• 1 centiliter is equal to 10 milliliters.
• To convert from milliliters to centiliters, you simply divide the number of milliliters by 10.

For example, to convert 750 milliliters into centiliters, you would perform the calculation: \[ \text{centiliters} = \frac{750 \text{ mL}}{10} = 75 \text{ cL} \] Understanding this conversion is helpful in various real-life situations, such as when dealing with European wine bottles, which are often quantified in centiliters.

Exploring the Metric System

The metric system is an internationally recognized system of measurement that is used in many regions around the world. It is based on the powers of ten, making it easy to convert between different units. For volume, the metric system uses a range of units including milliliters (mL), centiliters (cL), and liters (L). Each step up or down in these units involves a factor of ten, which simplifies the conversion process.

• 1 milliliter (mL) = 0.1 centiliters (cL)
• 1 centiliter (cL) = 10 milliliters (mL)
• 1 liter (L) = 100 centiliters (cL)

This logical structure of the metric system is one reason why it’s preferred in scientific communities and used widely for everyday applications, from cooking to industrial settings.

Volume Conversion in Everyday Contexts

Converting volumes is a practical skill that finds use in various activities such as cooking, pharmaceuticals, and even wine purchasing. Knowing how to switch between different volume units can enhance your understanding and efficiency in these tasks. Let's consider wine bottles in Europe; they are typically labeled in centiliters. If you need to buy a European wine bottle with a volume in a different unit, like milliliters, being able to convert accurately ensures that you understand what you're buying.For example, a standard wine bottle in many parts of the world might be labeled as 750 mL. If you know the conversion, you can easily determine that this equals 75 cL, as seen in the conversion process:\[ \text{centiliters} = \frac{750 \text{ mL}}{10} = 75 \text{ cL} \]Such competency in handling conversions aids in global trade and communication, bridging differences in measurement systems effortlessly.