Problem 22 - 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. \(969 \mathrm{m}\) to kilometers

Step-by-Step Solution

Answer

969 meters is equal to 0.969 kilometers.

Step 1: Understanding the Conversion Factor

To convert from meters to kilometers, you need to know the conversion factor between these two units. There are 1,000 meters in a kilometer. This means that to convert meters to kilometers, we will divide the number of meters by 1,000.

Step 2: Setting up the Conversion Equation

You have 969 meters that need to be converted into kilometers. Using the conversion factor, we set up the equation: \[ \text{kilometers} = \frac{969 \, \text{meters}}{1000} \] This equation allows us to convert meters into kilometers by dividing by 1,000.

Step 3: Performing the Division

Now, perform the division as set up in the equation: \[ \frac{969}{1000} = 0.969 \] The result is 0.969 kilometers.

Step 4: Reviewing the Solution

To ensure accuracy, verify that dividing by 1,000 is the correct conversion method from meters to kilometers, which it is. Therefore, 969 meters is equal to 0.969 kilometers.

Key Concepts

Metric Units

The metric system is a standardized system of measurement used worldwide. It is designed to simplify calculations and conversions through a decimal-based format. The system includes units like meters, kilograms, and liters. In this system, different measurements are interconnected through multiples of ten, making it easy to scale up or down using powers of ten.

• Meters (m): The primary unit of length.
• Kilometers (km): Used for longer distances, where 1 kilometer equals 1,000 meters.

Understanding metric units is crucial for making accurate conversions. Each unit increase or decrease by a factor of ten means that calculations often involve simply moving the decimal point. This makes the metric system exceptionally user-friendly.

Conversion Factor

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. In the metric system, these factors are based on powers of ten. When converting meters to kilometers, the conversion factor is 1,000.

• To go from a smaller unit (meters) to a larger unit (kilometers), divide by the conversion factor.
• To convert back (from kilometers to meters), multiply by the conversion factor.

For our exercise, converting 969 meters to kilometers involves dividing by the conversion factor of 1,000. This approach simplifies the process significantly, by transforming complex conversions into elementary arithmetic operations, which helps prevent errors.

Decimal Division

Decimal division is a method used to divide numbers that include decimals. In metric conversions, it often involves moving a decimal point. For the exercise at hand, converting 969 meters to kilometers requires dividing 969 by 1,000.
When you divide 969 by 1,000, you effectively shift the decimal point three places to the left, making it 0.969.

• Before division: 969 (this is like having the decimal point after the whole number as in 969.0)
• After division: 0.969 (the decimal shifts leftward by three positions)

This simple shift is a key concept in understanding metric system conversions, facilitating ease in numerical transformation. It is important to note how decimal movement correlates directly with the factors of ten in the metric system.