Problem 2 - 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. \(9 \mathrm{ft}\) to inches

Step-by-Step Solution

Answer

9 feet is 108 inches.

Step 1: Identify Conversion Factor

To convert feet to inches in the U.S. system, we need to know the conversion factor. There are 12 inches in 1 foot.

Step 2: Multiply by Conversion Factor

Use the conversion factor to convert 9 feet into inches. Multiply 9 by 12.

Step 3: Perform the Calculation

Calculate the product: \[ 9 \times 12 = 108 \]

Step 4: Write the Answer

The answer to the conversion is that 9 feet is equal to 108 inches.

Key Concepts

Units of Measurement

Units of measurement are essential for quantifying physical quantities. They help provide clarity and precision. In the U.S. system, measurements such as feet and inches are commonly used for measuring length.

Feet and inches belong to the same category of units known as imperial units. One foot is equivalent to 12 inches. Understanding this relationship is crucial for conversions within the system.

These conversions are based on standards and definitions that ensure uniformity across different regions and applications. They allow us to express measurements in a format that might be more convenient or required for specific tasks.

Conversion Factors

A conversion factor is a ratio used to express the same quantity in different units. It acts as a bridge that connects different units, helping us translate one measurement into another efficiently. In the exercise provided, the conversion factor from feet to inches is 12. This means every foot contains 12 inches.

Understanding why we need this conversion is important. Let's say you're measuring a room, and you need the measurement in inches for precise interior design placement or construction work. That's where knowing the conversion factor comes in handy.

The beauty of conversion factors is their simplicity and practicality. Once you remember that 1 foot equals 12 inches, you can convert any measurement from feet to inches by simply multiplying by 12. Conversion factors are not restricted to length alone; they can apply to any measurable quantity such as volume, weight, or temperature.

Problem-Solving Steps

Problem-solving steps in unit conversion follow a systematic approach to ensure accuracy. This process involves several straightforward steps.

• **Identify the units involved**: Determine the initial unit (feet) and the unit you want to convert into (inches).
• **Note the conversion factor**: In this case, 1 foot equals 12 inches.
• **Perform the calculation**: Multiply the original measurement (9 feet) by the conversion factor (12). The calculation results in 108 inches.
• **Present the answer**: Clearly state that the conversion from 9 feet resulted in 108 inches.

Each of these steps helps break down the task into manageable parts. This systematic method reduces errors and enhances understanding. It transforms what might seem intimidating at first glance into a simple task that can be tackled with confidence.