Problem 52 - Prealgebra

Question

Set up the following conversions as you have been doing. Then perform the calculations on a calculator. Change 379 millimeters to kilometers.

Step-by-Step Solution

Answer

379 millimeters is equal to 0.000379 kilometers.

Step 1: Understand the Problem

We are tasked with converting a measurement from millimeters (mm) to kilometers (km). A conversion involves changing a value from one unit to another.

Step 2: Know the Conversion Factors

We need the conversion between millimeters and kilometers. We know that: - 1 millimeter (mm) = 0.001 meters (m) - 1 kilometer (km) = 1000 meters (m)

Step 3: Convert Millimeters to Meters

First, convert 379 millimeters into meters using the conversion factor:\[379 \text{ mm} \times 0.001 \frac{\text{m}}{\text{mm}} = 0.379 \text{ m}\]

Step 4: Convert Meters to Kilometers

Now, convert the result from meters to kilometers using the conversion factor:\[0.379 \text{ m} \times \frac{1 \text{ km}}{1000 \text{ m}} = 0.000379 \text{ km}\]

Step 5: Finalize the Conversion

Thus, 379 millimeters is equal to 0.000379 kilometers.

Key Concepts

Millimeters to Kilometers

When converting measurements, it's crucial to understand the units you're working with. In this case, we're converting millimeters (mm) to kilometers (km), which are both units of length. Millimeters are typically used to measure smaller lengths, while kilometers are used for longer distances.

Steps for Converting:

• First, recognize that 1 mm is much smaller than 1 km.
• Understand that you will first need to convert millimeters to meters and then meters to kilometers.
• This multiphase conversion is essential because we're going from a smaller unit to a much larger one.

By following these steps, you'll have a straightforward way to handle and understand conversions between millimeters and kilometers.

Conversion Factors

Conversion factors are numbers used to change one set of units to another, while maintaining the actual size of the measurement. They are critical in ensuring that the numerical value reflects the correct relationships between the units.

Key Conversion Factors in the Exercise:

• 1 millimeter = 0.001 meters
• 1 kilometer = 1000 meters

These factors allow you to bridge different scales, for instance, going from a thousandths of a meter (mm) to thousands of meters (km).

Conversion factors require attention to ensure that your units cancel out properly. When you multiply or divide by these factors, pay careful attention to the units as well, ensuring they align correctly for a smooth conversion.

Prealgebra Problems

In prealgebra, conversion problems like the one provided serve as an introduction to understanding and working with units and scales. These problems develop your ability to perform basic arithmetic operations with real-world applications.

Prealgebra Problem Solving Strategies:

• Break down the problem into smaller, manageable steps.
• Understand each component, like the unit conversion factors.
• Perform calculations step-by-step, ensuring units consistently align correctly throughout your work.

Prealgebra problems build a foundation that prepares you for more advanced math, giving you the tools to tackle increasingly complex mathematical challenges with confidence.