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Chapter 8: Problem 37

Complete. Do as much as possible mentally. 392 dam = ________km

Short Answer

Expert verified
3.92 km

Step by step solution

01

Understand the unit conversion

We need to convert decameters (dam) to kilometers (km). Remember that 1 kilometer (km) equals 100 decameters (dam).
02

Set up the conversion

Use the conversion factor that 1 km = 100 dam. To convert from dam to km, we divide the number of decameters by 100.
03

Perform the division

Divide 392 dam by 100: \[\text{kilometers} = \frac{392 \text{ dam}}{100} = 3.92 \text{ km} \]
04

Write the final answer

After performing the division, we find that 392 dam equals 3.92 km.

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Key Concepts

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

decameters to kilometers conversion
Converting decameters (dam) to kilometers (km) is a straightforward process if you understand the relationship between the units. Both decameters and kilometers are part of the metric system, which means they share a basic conversion principle.
To convert from decameters to kilometers, remember that 1 kilometer is equal to 100 decameters.
  • 1 km = 100 dam
In our exercise, we need to convert 392 dam to kilometers.
division in unit conversion
To convert 392 decameters to kilometers, we use division. We apply the conversion factor between the units, where 1 kilometer equals 100 decameters. Because we are moving to a larger unit (kilometers from decameters), we divide.
Here's the basic formula: \[ \text{kilometers} = \frac{\text{number of decameters}}{100} \]
So for our specific problem: \[ \text{kilometers} = \frac{392}{100} = 3.92 \]
This means 392 decameters converts to 3.92 kilometers.
basic mathematics operations
Understanding basic mathematics operations is crucial in unit conversion. In this exercise, we used division, which is one of the core operations. Division in unit conversion involves dividing the numerical value by the conversion factor.
In our example, we divided 392 by 100 to convert from decameters to kilometers. Knowing how to perform this division is key to solving similar problems.
  • Step 1: Identify the units you are converting from and to.
  • Step 2: Use the appropriate conversion factor (e.g., 1 km = 100 dam).
  • Step 3: Perform the division to find your answer.
Practicing these steps will help you become more comfortable with unit conversions and basic math operations.

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