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Chapter 9: Problem 67

\(15 \mathrm{~km}-2360 \mathrm{~m}\)

Short Answer

Expert verified
12 km and 640 meters.

Step by step solution

01

Convert Units

First, we need to convert all measurements to the same unit. Since the distances are given in kilometers (km) and meters (m), we will convert kilometers to meters for consistency. 1 km is equal to 1000 meters. Thus, 15 km is equal to 15,000 meters.
02

Perform the Subtraction

Now that both measurements are in meters, subtract the smaller measurement from the larger one. Our calculation is: 15,000 meters - 2360 meters = 12,640 meters.
03

Convert Back to Kilometers and Meters

Convert the result back to kilometers and meters for a more intuitive understanding as needed. Since 1 km is 1000 meters, 12,640 meters can be expressed as 12 km and 640 meters.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Metric System
The metric system is an international decimal system of measurement that is used by most of the world. It is based on powers of ten, making calculations easier to perform. In the context of our problem, we deal primarily with kilometers and meters.
  • A kilometer (km) is 1,000 meters (m).
  • Both are units of distance in the metric system, which includes units like centimeters (cm), liters for volume, and grams for mass.

The clear advantage of the metric system is this uniformity, which simplifies unit conversion significantly. By knowing that 1 km equals 1,000 meters, we can easily switch between larger and smaller units without complex calculations.
Subtraction with Units
When you subtract measurements with units, it is crucial to ensure they are in the same unit. This ensures accuracy and prevents common mistakes. In our exercise, we started with kilometers and meters.

Here's why converting is important:
  • 15 kilometers needs to be converted to meters to directly subtract from 2,360 meters.
  • After conversion, the problem becomes a simple arithmetic operation: \(15,000 \text{ meters} - 2,360 \text{ meters} = 12,640 \text{ meters}\).

Converting back, if needed, can offer clarity, especially in contexts where certain unit representations are more common or intuitive, like expressing longer distances in kilometers and shorter in meters.
Distance Measurement
Distance measurement fundamentally involves determining how far apart two points are. In our exercise, we're essentially figuring out the remaining distance after a subtraction operation.

For practical purposes:
  • Distances like city-to-city travel might use kilometers.
  • Where precision is necessary, such as in construction, meters might be preferred.

Understanding the units appropriate for your context is crucial. In converting and adjusting units, you refine the precision of your measurements. For instance, while subtracting distances, maintaining consistency and clarity in unit representation ensures the accuracy of your end result.

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