Problem 20 - 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. 12 dm to millimeters

Step-by-Step Solution

Answer

12 dm is equal to 1200 mm.

Step 1: Understanding the Units

We are given a length measurement of 12 decimeters (dm) and need to convert it to millimeters (mm). To do this, we need to understand the relationship between decimeters and millimeters.

Step 2: Determine the Conversion Factor

In the metric system, 1 decimeter is equal to 100 millimeters. This conversion factor (100) tells us how many millimeters are in each decimeter.

Step 3: Apply the Conversion Factor

Multiply the number of decimeters by the conversion factor to convert the length measurement to millimeters.\[ 12 ext{ dm} imes 100 ext{ mm/dm} = 1200 ext{ mm} \]

Step 4: Write the Answer

The conversion of 12 decimeters to millimeters is 1200 millimeters. We expressed the answer as a whole number, as instructed.

Key Concepts

Metric Units

The metric system is a universal method of measurement used around the world due to its simplicity and ease of conversion. This system is based on the number 10, making it extremely convenient for converting between different units.

Common units of measurement in the metric system include:

• Millimeters (mm)
• Centimeters (cm)
• Decimeters (dm)
• Meters (m)
• Kilometers (km)

By using a common base of 10, conversions within the metric system become a matter of shifting decimal points, which is much simpler than non-metric systems. Whether measuring length, mass, or volume, the metric system provides consistency across calculations.

Conversion Factors

Conversion factors are a key concept in understanding metric conversions. These factors indicate how many of one unit fit into another. They are derived directly from the definitions of metric units. When converting between metric units, such as from decimeters to millimeters, the conversion factor tells us how many millimeters are equivalent to one decimeter.

A conversion factor is simply used by multiplying the quantity in the original unit by the conversion factor. This is computed through an equivalency such as:

• 1 decimeter is 100 millimeters, thus the conversion factor is 100.
• This means multiplying any decimeter measurement by 100 will convert it into millimeters.

Using conversion factors minimizes mistakes and makes the conversion process smooth and reliable.

Decimeters to Millimeters

Understanding how to convert decimeters to millimeters is a practical skill that demonstrates the application of conversion factors in the metric system. Here, we use the conversion factor: 100 millimeters per decimeter. This is because within the metric system, each decimeter comprises precisely 100 millimeters. This relationship is straightforward due to the decimal base of the metric system.

For example, to convert 12 decimeters to millimeters, multiply 12 by 100. This results in: \[ 12 \times 100 = 1200 \, \text{mm} \] This shows that 12 decimeters are equal to 1200 millimeters.

Practicing such conversions enhances your comfort with the metric system and helps you accurately work with different units of measurement.