Problem 28 - 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. \(89.5 \mathrm{cm}\) to decimeters

Step-by-Step Solution

Answer

89.5 cm is equal to 8.95 decimeters.

Step 1: Understanding the Units

We begin by identifying the units involved in the conversion. We have centimeters and decimeters. Our goal is to convert from centimeters to decimeters.

Step 2: Determine the Conversion Factor

In the metric system, 1 decimeter is equal to 10 centimeters. Therefore, to convert from centimeters to decimeters, we use a conversion factor of \(\frac{1 \text{ decimeter}}{10 \text{ centimeters}}\).

Step 3: Apply the Conversion Factor

Now, to convert 89.5 centimeters to decimeters, we multiply by the conversion factor:\[89.5 \text{ cm} \times \frac{1 \text{ decimeter}}{10 \text{ centimeters}} = 8.95 \text{ decimeters}\]This calculation involves multiplying 89.5 by 1/10, or simply dividing by 10.

Key Concepts

Length Conversion

Length conversion is a common task when dealing with measurements. It involves changing a measurement from one unit to another while maintaining its size in terms of magnitude. In our exercise, we're converting centimeters to decimeters.

When performing length conversions, we rely on a known relationship between the units. For example:

• 1 kilometer is 1000 meters
• 1 meter is 100 centimeters
• 1 centimeter is 10 millimeters

Understanding these relationships is crucial in making accurate conversions without changing the meaning of the measurement. By knowing these conversion factors, you can confidently convert between units in the metric system. This skill is essential, especially in scientific calculations and everyday measurements.

Centimeters to Decimeters

Converting from centimeters to decimeters is straightforward due to the simplicity of the metric system. The metric system is a base-ten system, which makes conversions easy and intuitive. Here's how centimeters and decimeters relate:

• 1 decimeter is equal to 10 centimeters.
• This means that the centimeter is smaller by a factor of 10 compared to the decimeter.

Thus, to convert from centimeters to decimeters, you divide by 10. For example, converting 89.5 centimeters into decimeters involves dividing by 10. You can think of it as moving the decimal point one place to the left. This gives us 8.95 decimeters. Such conversions are especially handy in situations where smaller units like centimeters need to be expressed in larger units for brevity or clarity.

Conversion Factor Calculation

Calculating the conversion factor is a key step in accurate conversions. A conversion factor is merely a ratio that expresses how many of one unit equals another unit within a particular measurement system. In our exercise, the conversion factor from centimeters to decimeters is determined as follows:

• 1 decimeter equals 10 centimeters.
• Thus, the conversion factor is \(\frac{1 \text{ decimeter}}{10 \text{ centimeters}}\).

To apply the conversion factor, you multiply the quantity you want to convert (in this case, 89.5 cm) by the conversion factor. This involves simple multiplication which, in essence, divides the number of centimeters by 10.
Conversion factors allow for an easy switch between units while maintaining the integrity of the measurement's magnitude. They are invaluable tools in any mathematician's or scientist's toolkit.