Problem 36 - Algebra 1: Concepts and Skills

Question

In Exercises \(32-37\), convert the units. Round the result to the nearest tenth. 100 yards to feet\((1 \text { yard }=3 \text { feet })\)

Step-by-Step Solution

Answer

100 yards is equal to 300 feet.

Step 1: Identify the Conversion Factor

From the problem, we know that 1 yard is equal to 3 feet. This is the conversion factor needed to convert yards to feet.

Step 2: Multiply the Number of Yards by the Conversion Factor

Using the conversion factor, multiply the number of yards by 3 to get the number of feet. So, \(100 \, \text{yards} \times 3 \, \text{feet/yard} = 300 \, \text{feet}\)

Step 3: Round to the Nearest Tenth

Although the conversion does not require any rounding in this case as the result is a specific number, had there been decimals, you would need to round the result to the nearest tenth.

Key Concepts

Understanding Conversion Factors

Conversion factors are essential tools in unit conversion. Simply put, a conversion factor allows you to convert measurements from one unit to another. It's a ratio that expresses how many of one unit are equivalent to another unit. For example, as given in our exercise, the conversion factor from yards to feet is 3. This means that one yard is equivalent to three feet.
When converting units:

• Identify the conversion factor you need. In this case, it's 1 yard = 3 feet.
• Make sure your units align correctly for the calculation.

The correct identification and application of the conversion factor make the difference between a successful conversion and a calculation mistake. This foundational concept not only applies to yards and feet but to any units you may need to convert.

Converting Yards to Feet

Converting yards to feet involves a straightforward multiplication process using our conversion factor. Since 1 yard equals 3 feet, to convert any number of yards to feet, you will multiply the number of yards by 3. For example, with 100 yards, the conversion process would be:

• Start with the number of yards: 100
• Multiply by the conversion factor (3 feet/yard): \(100 \text{ yards} \times 3 \text{ feet/yard} = 300 \text{ feet} \)

This calculation shows that 100 yards are equal to 300 feet. Understanding this step involves ensuring that multiplication is done correctly and that you apply the conversion factor consistently. It's a simple yet critical exercise in basic unit conversion.

Rounding Numbers

Rounding numbers involves approximating a number to make it simpler while keeping it close to the original value. In the context of this exercise, you might need to round if your conversion result is a decimal. Rounding numbers to the nearest tenth means looking at the hundredths digit:

• If it's 5 or more, round up.
• If it's less than 5, round down.

For example, if your conversion calculation resulted in 307.56 feet, you'd round it to 307.6 feet. However, in this particular conversion, we ended with the whole number 300, so there was no need to round. But it's good practice to check, especially when decimals are involved, to ensure accuracy in your conversions.