Problem 31 - Elementary Algebra

Question

Evaluate \(8 \mathrm{~km}+4 \mathrm{~m}\). Write the answer in meters.

Step-by-Step Solution

Answer

8004 meters

Step 1 - Understand the Units Involved

The problem involves two different units: kilometers (km) and meters (m). To consolidate these, both quantities need to be in the same unit. Here, we will convert kilometers to meters.

Step 2 - Convert Kilometers to Meters

Use the conversion factor that 1 kilometer is equal to 1000 meters. Thus, to convert 8 kilometers to meters, multiply by 1000:\[ 8 \text{ km} \times 1000 \frac{\text{m}}{\text{km}} = 8000 \text{ m} \]

Step 3 - Add the Meters Together

Now both measurements are in meters. Add the converted kilometers (8000 meters) to the existing meters (4 meters):\[ 8000 \text{ m} + 4 \text{ m} = 8004 \text{ m} \]

Key Concepts

kilometers to meters conversion

When converting between kilometers and meters, we rely on the metric system's base units. A kilometer is a larger unit than a meter. Specifically, 1 kilometer is equal to 1000 meters. This conversion is straightforward. To convert kilometers into meters, simply multiply the number of kilometers by 1000.

For example, if you have 8 kilometers, you multiply 8 by 1000 to get 8000 meters. So:

• 8 km × 1000 = 8000 m

This kind of conversion is very common and useful in various real-world situations, such as measuring distances for travel or in scientific calculations.

Always ensure you keep track of your units during conversions to avoid errors.

adding measurements

Adding measurements is a fundamental concept when dealing with quantities in the same unit. Once all quantities are converted to the same unit, the process becomes simple.

Let's say you have two measurements: 8000 meters and 4 meters. To combine these, you just add them together:

• 8000 m + 4 m = 8004 m

This addition is straightforward because both quantities are now expressed with the same unit. Mixing units without conversion can lead to confusion and incorrect results.

Understanding this process is crucial for problem-solving in math, science, and everyday life. Always ensure that all measurements are in the same unit before performing addition or other operations.

metric system conversion

The metric system is an internationally agreed decimal system of measurement. It simplifies calculations and conversions through its use of base ten units.

Understanding the basics of metric conversions like kilometer to meter (1 km = 1000 m) is essential. Common metric units include:

• Millimeters (mm)
• Centimeters (cm, 1 cm = 10 mm)
• Meters (m, 1 m = 100 cm)
• Kilometers (km, 1 km = 1000 m)

Using these straightforward conversions, you can easily switch between units.

Practicing these conversions and understanding the relationships between metric units will build a strong foundation for more complex calculations you might encounter in science, engineering, and everyday tasks.