Problem 26 - Prealgebra

Question

Make the following conversions in the metric system by multiplying by the appropriate conversion factor. Write your answers as whole numbers or decimals. \(4,388 \mathrm{dm}\) to meters

Step-by-Step Solution

Answer

4,388 dm is equal to 438.8 m.

Step 1: Understand the Units of Conversion

The problem asks to convert decimeters (dm) to meters (m). We know from the metric system that 1 meter is equal to 10 decimeters.

Step 2: Set Up the Conversion Factor

We need to convert decimeters to meters, so we will use the conversion factor \ \(1 \, \text{m} = 10 \, \text{dm} \). To convert from dm to m, you divide by 10.

Step 3: Perform the Conversion

To convert 4,388 dm to meters, divide the number of decimeters by 10: \[4,388 \, \text{dm} \times \frac{1 \, \text{m}}{10 \, \text{dm}} = 438.8 \, \text{m}\]

Step 4: Write the Result

Conclude the conversion with the final answer: 4,388 dm is equal to 438.8 m.

Key Concepts

Understanding Decimeters to Meters

The task of converting decimeters to meters may seem complicated at first, but it is actually straightforward once you understand the basic relationship between the two units. In the metric system, the prefix 'deci-' signifies a factor of one-tenth. Therefore, a decimeter (dm) is one-tenth of a meter (m). This makes it easy to convert decimeters directly to meters:

• 1 meter = 10 decimeters
• To convert from decimeters to meters, you divide the number of decimeters by 10

Using this conversion rule, you simply take the total number of decimeters and perform a division by 10 to find the equivalent in meters. For example, if we need to convert 4,388 decimeters into meters, the calculation would be: \[4,388 \text{ dm} \div 10 = 438.8 \text{ m}\] With this simple process, you can quickly and accurately perform conversions from decimeters to meters.

The Basics of Unit Conversion

Unit conversion is an essential skill in many fields, from science to construction. It involves transforming a quantity expressed in one unit to an equivalent quantity in a different unit. To achieve this, you multiply or divide by a conversion factor, which is a number used to change one unit of measurement to another. Here's how it works:

• Identify the units you are converting between.
• Determine the conversion factor.
• Perform the necessary multiplication or division using the conversion factor.

For decimeters to meters, the conversion factor is 1 meter = 10 decimeters. This means you divide the number of decimeters by 10 to convert to meters. It's crucial to always ensure that the units cancel each other properly in your calculation, leaving you with the desired units in the answer. Understanding this process helps you avoid mistakes and ensures accuracy in any unit conversion task you encounter.

The Metric System Explained

The metric system is an internationally adopted system of measurement that is based on powers of ten. It is widely used around the world and provides a simple way of dealing with measurements. Distances, volumes, weights, and many other quantities can be expressed conveniently in this system. Key features of the metric system include:

• Units are based on powers of ten, making calculations straightforward.
• Common prefixes like kilo-, centi-, and milli- indicate different scales or magnitudes.
• It is used universally, which facilitates international communication and understanding.

Each unit in the metric system can be easily converted to another. For instance, 1000 grams make a kilogram, and 100 centimeters make a meter. This system is not only easier to use than non-metric systems but also allows for higher precision and ease in scientific calculations.