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

40 mL

Step 1: Understand the Decimal

The phrase 'four hundredths' of a liter refers to the fraction or decimal representation of 0.04 liters.

Step 2: Identify the Correct Metric System Unit

In the metric system, volume is typically measured in liters (L). For smaller volumes, milliliters (mL) are commonly used. Since 1 liter equals 1000 milliliters, we need to convert portion of a liter to milliliters.

Step 3: Set Up the Conversion Equation

The decimal 0.04 liters can be converted to milliliters by multiplying by 1000, because there are 1000 milliliters in a liter.

Step 4: Perform the Conversion Calculation

Calculate the conversion: \( 0.04 \text{ L} \times 1000 = 40 \text{ mL} \).

Step 5: Write the Answer in the Correct Form

The final answer is 40 milliliters or abbreviated as 40 mL, which is the proper metric abbreviation.

Key Concepts

Conversion Calculation

Conversion calculation is a fundamental process in the metric system that enables us to express measurements in different units while maintaining their original value. This process often requires the use of conversion factors, which provide the ratio needed to convert from one unit to another.
To perform a conversion calculation, it is essential to

• Identify the original value and its unit.
• Determine the desired unit for conversion.
• Use a known conversion factor to perform the calculation.

In the provided exercise, we are converting liters to milliliters. The conversion factor here is 1000 because there are 1000 milliliters in one liter. To calculate this conversion, multiply the original metric measurement by the conversion factor: 0.04 liters multiplied by 1000 gives us 40 milliliters. This method ensures accuracy without altering the physical quantity's value.

Metric Units

Metric units are a standardized system that simplifies measurements across the globe. The metric system is based on units of ten, making conversions straightforward and easier to understand. Some key advantages of using metric units include their consistency and simplicity due to its base ten structure.
In the context of volume, the primary unit is the liter. For smaller quantities, the milliliter is more convenient, as seen in our exercise where 0.04 liters is expressed as 40 milliliters. One can easily convert between various metric units by using their respective conversion factors. Other common metric units include meters for length, grams for mass, and seconds for time. These units form a comprehensive measurement system used in both scientific and everyday contexts.

Volume Measurement

Volume measurement is crucial in various fields, such as chemistry, cooking, and medicine, where precise amounts are essential. Volume measures the amount of space occupied by a substance, and in the metric system, the liter is the standard unit. For small volumes, such as in our exercise, milliliters provide a practical alternative.
Understanding volume measurement involves knowing these key points:

• 1 liter equals 1000 milliliters.
• Milliliters are typically used for small liquid volumes.
• For very large volumes, kiloliters may be used, where 1 kiloliter equals 1000 liters.

In our example, calculating that 0.04 liters is 40 milliliters demonstrates a straightforward approach to measure small liquid quantities accurately. Mastering volume measurements ensures precision in experiments, recipes, and various calculations.