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Chapter 1: Problem 863

Convert the units. Mount Whitney is 3,072 meters tall. Convert the height to kilometers.

Short Answer

Expert verified
Mount Whitney is 3.072 kilometers tall.

Step by step solution

01

- Understand the Relationship

There are 1,000 meters in 1 kilometer. This means that to convert meters to kilometers, you need to divide the number of meters by 1,000.
02

- Perform the Division

Take the height of Mount Whitney, 3,072 meters, and divide it by 1,000 to convert it to kilometers. \[ \text{Height in kilometers} = \frac{3072}{1000} \ = 3.072 \text{ kilometers} \]

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Key Concepts

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

meters to kilometers conversion
Meters and kilometers are units used to measure length in the metric system. When we need to convert meters to kilometers, we use the relationship that exists between them. Specifically, 1 kilometer is equal to 1,000 meters.
This conversion is straightforward because both meters and kilometers are based on the base-10 system. So, if you know the number of meters, you can convert it easily to kilometers by dividing by 1,000. For example, if you have 3,072 meters, you divide it by 1,000 to get 3.072 kilometers.
Remember that converting from meters to kilometers is practical in science, geography, and everyday life, allowing us to describe distances and heights more conveniently.
division for conversion
The main mathematical operation used in the conversion from meters to kilometers is division. Since there are 1,000 meters in 1 kilometer, we divide the number of meters by 1,000. This is a simple yet critical step.
For instance, converting 3,072 meters to kilometers involves dividing 3,072 by 1,000:
\ \[ \text{Height in kilometers} = \frac{3072}{1000} = 3.072 \text{ kilometers} \]
By performing this division, we effectively scale down the larger unit (meters) to a smaller, more manageable number (kilometers). Division for conversion is a fundamental technique that applies to many unit conversions, making this concept essential for handling various measurement topics.
metric system basics
Understanding the metric system is crucial for efficiently converting units. The metric system is used globally and is based on powers of ten, which simplifies calculations.
Key units of length in the metric system include millimeters (mm), centimeters (cm), meters (m), and kilometers (km). These units correlate as follows:
  • 1 kilometer = 1,000 meters
  • 1 meter = 100 centimeters
  • 1 centimeter = 10 millimeters
This structure means that converting between these units often requires simple multiplication or division by 10, 100, or 1,000.
By understanding how these units interact, as demonstrated in the meters to kilometers conversion, you can easily move between different scales of measurement within the metric system.

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