Problem 21 - 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. \(248 \mathrm{m}\) to kilometers

Step-by-Step Solution

Answer

248 meters is 0.248 kilometers.

Step 1: Identify the conversion factor

To convert meters to kilometers, recall that 1 kilometer equals 1000 meters. Thus, the conversion factor needed is 1 km/1000 m.

Step 2: Set up the conversion equation

We need to multiply the given value in meters by the conversion factor to convert it to kilometers. The equation will be: \[\text{Distance in km} = 248 \text{ m} \times \frac{1 \text{ km}}{1000 \text{ m}}\]

Step 3: Perform the multiplication

Multiply the distance in meters (248 m) by the conversion factor (1 km/1000 m) to determine the distance in kilometers.\[248 \text{ m} \times \frac{1 \text{ km}}{1000 \text{ m}} = 0.248 \text{ km}\]

Step 4: Write the final answer

The distance of 248 meters is equivalent to 0.248 kilometers. This is expressed as a decimal, which accurately represents the conversion.

Key Concepts

Understanding Conversion Factors

Conversion factors are crucial to converting units from one system to another, like going from meters to kilometers. A conversion factor is simply a ratio that expresses how many of one unit equals another unit. It's like a bridge that helps us translate measurements into the desired unit. For instance, 1 kilometer is the same as 1000 meters. This can be written as a fraction, or more precisely, a conversion factor:

• 1 km = 1000 m
• Conversion factor: \( \frac{1 \text{ km}}{1000 \text{ m}} \)

Using the conversion factor involves multiplication. This helps us switch from one unit to another without changing the actual quantity being measured. When you multiply a measurement by this factor, it scales the number to a new unit without altering the measurement's size. It keeps the numerical relationship intact but alters the unit for clarity or preference.

Converting Kilometers to Meters

The metric system often requires us to switch from larger units like kilometers to smaller units like meters and vice versa. This process is straightforward because the relationship is linear; 1 kilometer contains exactly 1000 meters. Therefore, converting between these involves simple multiplication or division by 1000.In our example problem, we're converting meters to kilometers. To do that:

• Identify the conversion factor: 1 km = 1000 m
• Set up your equation: \( \text{Distance in km} = \text{Distance in m} \times \frac{1 \text{ km}}{1000 \text{ m}} \)
• Calculate: 248 m becomes 0.248 km

This sequence allows us to shift from meters (a smaller-scale view) to kilometers (a larger-scale view) accurately, using multiplication by a fraction that encodes the relationship between kilometers and meters.

Importance of Decimal Representation

Writing answers as decimals, especially in the context of metric conversions, provides precision and clarity in expressing measurements. When converting units, often the result is not a whole number. Instead, it’s a part or fraction of the unit, which is where decimal representation comes in really handy. In our exercise, the calculated distance of 248 meters converts to 0.248 kilometers. This decimal answer:

• Conveys exactness which is crucial in many fields like engineering, science, and construction
• Shows the precise relation as decimals naturally express quantities between whole numbers
• Is simple to understand and use for further calculations as decimals integrate well into different mathematical operations

Decimals bridge the gap between numbers and practicality, ensuring precise communication of metric results from one form to another.