Problem 19 - Calculate With Confidence

Question

Using abbreviations and the rules of the metric system, express the following quantities correctly. Four hundredths of a liter ________

Step-by-Step Solution

Answer

4 cl

Step 1: Understand the Given Quantity

We need to express 'four hundredths of a liter' correctly using metric units. The root word here is 'liter', which is a common unit for measuring volume.

Step 2: Determine the Decimal Representation

Four hundredths means the quantity is equal to 0.04. So, we have 0.04 liters.

Step 3: Identify the Corresponding Metric Prefix

The metric system uses prefixes to denote powers of ten. We need a prefix for 0.04 liters. Since 1 liter is 100 centiliters, 0.04 liters can be expressed as 4 centiliters because 0.04 liters = 4 cl.

Step 4: Apply the Appropriate Metric Abbreviation

The abbreviation for centiliters is 'cl'. Therefore, four hundredths of a liter is expressed as 4 cl.

Key Concepts

Metric Prefixes

In the metric system, prefixes are used to express quantities in different powers of ten. This helps to simplify numbers, making them more manageable and easy to understand. For instance, in the metric system, a meter can be divided into smaller parts called centimeters or larger parts called kilometers. The most commonly used metric prefixes include:

• Kilo- (k) which indicates a factor of 1,000
• Hecto- (h) means 100
• Deka- (da) represents 10
• Deci- (d) is one-tenth (0.1)
• Centi- (c) represents one-hundredth (0.01)
• Milli- (m) is one-thousandth (0.001)

These prefixes provide a clear way to communicate very large or very small quantities. Knowing them can make it much easier to work with metric measurements, both in scientific contexts and everyday life.

Volume Measurement

Volume measurement in the metric system often involves the use of liters. A liter is a standard unit for measuring liquids, such as water, milk, and other beverages. It is widely utilized due to its convenience in everyday life. There are different sizes of volumes in metric units such as:

• Milliliters (ml): 1,000 milliliters make 1 liter
• Centiliters (cl): 100 centiliters are equivalent to 1 liter
• Deciliters (dl): 10 make up 1 liter

Understanding these units and their conversions is crucial for tasks that involve measuring volumes, like cooking or laboratory work. The use of the metric system ensures accuracy and unambiguity, which are important in many practical applications.

Decimal Conversion

Decimal conversion is the process of changing a number to a decimal form. To express quantities like 'four hundredths' of a liter in decimals, we transform the word form to numeric form as 0.04. A few points about decimal conversion include:

• Tenths are represented as numbers with a single digit after the decimal point (e.g., 0.1).
• Hundredths are written with two digits after the decimal point (e.g., 0.04).
• Thousandths would be shown with three digits after the decimal point.

Being comfortable with decimal conversions ensures that you can easily switch between different ways of representing the same value, which is essential in learning to handle finer and larger measurements.

Metric Abbreviations

Metric abbreviations are shorthand symbols representing metric units. They make it quicker and easier to write down measurements. It’s essential to remember that each metric unit has a universal abbreviation, facilitating international communication and understanding. Some common metric abbreviations include:

• "m" for meters
• "g" for grams
• "l" for liters
• "ml" for milliliters
• "cl" for centiliters

Using the correct abbreviation, such as "cl" for centiliters, helps maintain precision and clarity, especially in contexts like science and commerce, where specific measurements are crucial. Consistently applying these conventions will help you gain accuracy and efficiency in working with metric measurements.