Problem 39 - Calculate With Confidence

Question

Convert the following metric measures by moving the decimal. \(5 \mathrm{~L}=\) ______\(\mathrm{mL}\)

Step-by-Step Solution

Answer

5 L equals 5,000 mL.

Step 1: Understand the Conversion

To convert from liters (L) to milliliters (mL), we need to understand the relationship between these units. By definition, 1 liter is equal to 1,000 milliliters.

Step 2: Set up the Conversion Factor

Since 1 L equals 1,000 mL, we will multiply the given number of liters by 1,000 to convert to milliliters. This means we multiply the quantity in liters by the conversion factor 1,000 mL/1 L.

Step 3: Perform the Conversion Calculation

Multiply 5 L by 1,000 to convert to milliliters:\[5 \, \text{L} \times 1,000 \, \frac{\text{mL}}{\text{L}} = 5,000 \, \text{mL}\]

Step 4: Move the Decimal Point

When multiplying by 1,000, you move the decimal point three places to the right. Since 5 can be written as 5.0, moving the decimal three places gives 5,000.0, or simply 5,000.

Key Concepts

Understanding Liters to Milliliters Conversion

Converting liters to milliliters is an essential skill in the metric system, which is a standardized way of measuring used around the world. In simple terms, to convert from liters (L) to milliliters (mL), you need to know the basic relationship between these two units.
One liter is equal to one thousand milliliters. This is because a milliliter is a smaller unit of volume compared to a liter, and precisely 1,000 mL make up 1 L. This relationship is crucial when you want to switch between these measurements.
For instance, if you have 5 liters of water, you simply think of 5 liters as five groups of 1,000 milliliters. So, multiplying gives you exactly 5,000 milliliters.

Decimal Point Movement in Metric Conversion

An essential trick in moving between metric units, like liters and milliliters, is using the decimal point. When converting a larger unit to a smaller one by multiples of ten, you can use decimal point movement.
Consider moving from liters to milliliters: the conversion involves multiplying by 1,000, which can be visualized as shifting the decimal point three spaces to the right.
Here's how it works:

• Identify the number in liters (e.g., 5.0).
• Move the decimal three spots to the right to account for each zero in 1,000.
• The number 5.0 becomes 5,000.0, simplifying to 5,000.

By practicing this method, conversion becomes a straightforward task without needing a calculator.

The Role of Conversion Factors in Mathematics

In mathematical conversions, a conversion factor is a crucial element. It allows you to change a measure from one unit to another in a reliable and consistent way.
When converting from liters to milliliters, the conversion factor used is 1,000 mL per 1 L. This fraction, while visually represents 1 (since 1,000 mL equals 1 L), is implemented to perform the conversion calculation.
The principle is straightforward:

• Take the original measurement (e.g., 5 L).
• Multiply by the conversion factor (1,000 mL/1 L).
• This gives you the new measurement (5,000 mL).

In essence, conversion factors maintain proportional consistency between units, ensuring accuracy in measurement changes.