Question

When you convert feet to inches, how do you decide which part of the conversion factor should be in the numerator and which in the denominator?

Short answer

Place the desired units in the numerator and the starting units in the denominator.

Step-by-step solution

Understand the Conversion Factor

The conversion factor between feet and inches is 1 foot = 12 inches.

Determine Starting Units

Identify the units you are starting with, which in this case is feet.

Define the Desired Units

Identify the units you want to convert to, which are inches.

Set Up the Conversion Factor with Correct Orientation

The conversion factor should be set up so that the units you are starting with are canceled out. Since you are starting with feet and want to convert to inches, the fraction should be set up as follows: \(\frac{12 \text{ inches}}{1 \text{ foot}}\). This allows feet to cancel out and leaves you with inches.

Perform the Conversion

Multiply the number of feet by the conversion factor placed appropriately: \(\text{number of feet} \times \frac{12 \text{ inches}}{1 \text{ foot}}\).

Key concepts

Conversion Factor

Conversion factors are used to change the units of a measurement without changing its value.
This involves multiplying or dividing by a fraction that equals 1. For example, when converting feet to inches, the conversion factor is 1 foot = 12 inches. Since 1 foot and 12 inches are the same length, their ratio is 1.

Conversion factors can be set up so that either the numerator or the denominator contains the unit you want to cancel out. This is key when performing dimensional analysis, which we'll cover next. Remember, the ultimate goal is to ensure the original unit cancels out, leaving you with the desired unit.

Dimensional Analysis

Dimensional analysis is a method used to convert one kind of unit to another.

The process involves using conversion factors set up as fractions to cancel out units step by step. Follow these steps for dimensional analysis:

• Identify the unit you are starting with (e.g., feet).
• Determine the unit you want to convert to (e.g., inches).
• Find a conversion factor that links the two units (e.g., 1 foot = 12 inches).
• Set up the conversion factor so that the starting unit cancels out.

By multiplying the starting measurement by the conversion factor, you cancel out the original unit, leaving you with the desired unit. This ensures your calculations remain accurate and your results are in the correct units.

Feet to Inches Conversion

To convert feet to inches, you need to set up the conversion factor correctly.

In this case, the conversion factor is 1 foot = 12 inches. Let's say you have 3 feet and want to know how many inches that is. Identify your starting unit (feet) and your desired unit (inches).
Then set up the conversion fraction to cancel out feet: \(\frac{12 \text{ inches}}{1 \text{ foot}}\).
Here's the process:

• Write down the number of feet: 3 feet
• Multiply by the conversion factor: 3 feet \(\times \frac{12 \text{ inches}}{1 \text{ foot}}\)
• The 'feet' units cancel out, leaving you with: 3 \(\times 12 \text{ inches}\)
• Solve: 3 \(\times 12 = 36 \text{ inches}\)

So, 3 feet is equal to 36 inches. By following these steps, you can easily convert feet to inches or any other units using the correct conversion factors.