Problem 19 - 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. \(5 \mathrm{dm}\) to centimeters

Step-by-Step Solution

Answer

5 dm is equal to 50 cm.

Step 1: Understand the Conversion Relationship

First, identify the conversion factor between decimeters (dm) and centimeters (cm). We know from the metric system that 1 dm is equal to 10 cm.

Step 2: Set Up the Equation

To convert from decimeters to centimeters, multiply the number of decimeters by the conversion factor. Since 1 dm = 10 cm, the equation to convert 5 dm to cm is: \[ 5 \text{ dm} \times 10 \text{ cm/dm} \]

Step 3: Perform the Calculation

Multiply the given number of decimeters by 10 to convert to centimeters: \[ 5 \times 10 = 50 \text{ cm} \]

Step 4: Write the Answer

The conversion of 5 dm to centimeters results in 50 cm. Thus, 5 dm is equal to 50 cm.

Key Concepts

Conversion Factor

In the world of measurements, a conversion factor is a helpful tool that allows us to switch units easily. It’s a number we multiply by to change a quantity from one unit to another. This is especially handy when working within the metric system. A conversion factor expresses the relationship between two different units.
For instance, the conversion factor from decimeters to centimeters is 10. This means that each decimeter is made up of 10 centimeters. So, when you know how many decimeters you have and want to find out the number of centimeters, you multiply by this conversion factor.

• Conversion Factor: A number used to change one unit to another.
• Example: 1 dm = 10 cm, so the conversion factor is 10.

Using conversion factors makes problems easier because you only need to multiply by a simple number. If you remember to check if you multiplied correctly, you’ve mastered the conversion step!

Decimeters to Centimeters

Switching from decimeters to centimeters involves a simple multiplication process. It’s straightforward once you understand the relationship between these units.
A decimeter is a unit of length measurement in the metric system. It is part of the series of units used globally because of its simplicity and ease of calculation. One decimeter is equal to 10 centimeters, forming a direct one-to-ten relationship.
When you want to convert, pick the number of decimeters you have and multiply by 10.

• 1 decimeter = 10 centimeters
• Multiply the number of decimeters by 10 to get centimeters

For example, if you have 5 decimeters and need to express it in centimeters, just do this:
Multiply 5 by 10, which equals 50. So, 5 decimeters is equivalent to 50 centimeters.

Metric System

The metric system is a global standard used for measurements. Developed for its ease and universal applicability, it was designed to replace the confusing system of units. It uses units like meters, grams, and liters.
What makes the metric system neat is its base-10 structure. This means that conversions typically involve multiplying or dividing by powers of ten, like 10, 100, or 1,000.

• Base units: meter, liter, gram
• Converting involves multiplying/dividing by 10, 100, 1,000, etc.
• Easier calculation due to its base-10 properties

It simplifies things enormously. Rather than working with random conversion values, the metric system keeps it straightforward. It’s consistent and predictable, and that's why dealing with conversions like decimeters to centimeters becomes a no-brainer! This system's straightforward nature is the reason for its worldwide popularity.