Problem 3 - Prealgebra

Question

Make the following conversions in the U.S. system by multiplying by the appropriate conversion factor. Write your answers as whole numbers or mixed numbers. \(10 \mathrm{ft}\) to inches

Step-by-Step Solution

Answer

10 feet is equal to 120 inches.

Step 1: Understand the Conversion Relationship

To convert feet to inches, we use the conversion factor that 1 foot is equal to 12 inches. This is a fundamental relationship needed to perform the conversion.

Step 2: Set Up the Multiplication

We will multiply the number of feet by the conversion factor to convert the measurement into inches. For this problem, our measurement in feet is 10. We have: \[ 10 \text{ ft} \times 12 \text{ inches/ft} \]

Step 3: Perform the Calculation

Carry out the multiplication from Step 2. Multiply 10 by 12 to find the equivalent in inches: \[ 10 \times 12 = 120 \] So, 10 feet is equivalent to 120 inches.

Step 4: Write the Answer Properly

Since the question asks for the answer in whole numbers or mixed numbers, and our result is a whole number, no further action is needed. The final answer is already appropriately formatted.

Key Concepts

Understanding the Conversion Factor

The conversion factor is a crucial component when dealing with unit conversions. It is a ratio that expresses how many of one unit are equivalent to another. In our example, converting feet to inches requires knowledge that 1 foot equals 12 inches. This conversion factor, **12 inches per foot**, is a constant used to transform any amount in feet to inches, simplifying the process exponentially.
One must always use the correct conversion factor for the units involved. When converting between units, ensuring accuracy is vital. An incorrect conversion factor can lead to significant errors in the final calculation.
To apply a conversion factor correctly:

• Identify the units you are converting from and to (e.g., feet to inches).
• Find the conversion factor for these units (e.g., 1 foot = 12 inches).
• Multiply the original measurement by this factor to get the new measurement.

Exploring the U.S. Customary System

The U.S. customary system is one of several systems of measurement used around the world. It is predominantly used in the United States and is based on a mix of historical systems of units. Unlike the metric system, which is decimal-based, the U.S. customary system includes units such as feet, inches, pounds, and gallons.
Here are some familiar U.S. customary units of length:

• Inch
• Foot (1 foot = 12 inches)
• Yard (1 yard = 3 feet)
• Mile (1 mile = 5280 feet)

Understanding how to navigate the U.S. customary system can be tricky, especially when it includes conversions like feet to inches, but it becomes manageable with practice. Knowing key conversion factors, like those between feet and inches, is essential for smooth calculations.

Grasping the Basics of Measurement

Measurement is the process of determining the size, length, or amount of something. It is a fundamental concept that applies to virtually every aspect of science and daily life. Different systems of measurement are used worldwide, and understanding how to work within these is vital.
In any measurement task:

• Identify the quantity to be measured.
• Select the appropriate unit of measurement based on your system (U.S. customary, metric, etc.).
• Use a tool or conversion factor to measure accurately.

In the context of our problem, the quantity is length, measured in feet, and then converted to inches. Bridging different measurement systems effectively requires precision and attention to detail. This ensures that calculations and conversions yield accurate and meaningful results.