Problem 33 - Algebra 1: Concepts and Skills

Question

In Exercises \(32-37\), convert the units. Round the result to the nearest tenth. 2 years to months

Step-by-Step Solution

Answer

2 years equates to 24 months.

Step 1: Identify the conversion factor

In order to convert years into months, a conversion factor must be applied. Knowing that 1 year consists of 12 months, the conversion factor is 1 year equals 12 months.

Step 2: Multiply the known value with the conversion factor

The task is to convert 2 years to months. Therefore, we will multiply 2 years with the given conversion factor, that is 2 years * 12 (Months per year).

Key Concepts

Conversion Factor

Understanding conversion factors is the key to successful unit conversions. A conversion factor is a ratio that expresses how many of one unit are equivalent to another unit. For example, in converting years to months, we know that 1 year is equal to 12 months. Thus, the conversion factor here is 12 months per year.

• First, identify the units you are converting from and to. In this case, from years to months.
• Next, ask yourself, "How many months are in one year?" The answer is 12 months.
• This means the conversion factor we use is 12 months for every 1 year.

Applying the correct conversion factor ensures that our calculations maintain their correctness and scale appropriately. Always verify the factor you plan to use by confirming the definitions of the units involved. Conversions often pivot on recognizing and accurately applying these factors.

Multiplication

Once we have identified the correct conversion factor, multiplication is the operation that allows us to transform the quantity into the desired unit. In our problem, we need to figure out how many months are in 2 years. With our conversion factor of 12 months per year, let's see how this is done:

• Start with the given number of years (here, 2 years).
• Multiply the number of years by the conversion factor: \[2 \text{ years} \times 12 \text{ months/year} = 24 \text{ months}\]

The process of multiplication not only scales the quantity according to the factor but also retains all physical unit concepts in the transformation. It's important to double-check that the units you intend to eliminate are in the correct position before multiplying. This leads to accurate and meaningful results.

Rounding Numbers

Rounding numbers is often the final step in solving real-world problems, allowing results to reflect appropriate precision. In many academic and professional contexts, rounding helps to communicate results more clearly. In our problem, we need to round to the nearest tenth. Let's see how this would apply if our multiplication resulted in a non-whole number.

• First, identify the decimal place to which you are rounding. In this case, the nearest tenth (one digit after the decimal point).
• If the number to the right of the desired decimal place is 5 or greater, round up.
• If it's less than 5, round down by leaving the target digit unchanged.

Although our specific example results in whole numbers (24 months), understanding rounding is crucial for handling more complex calculations. Precise rounding depends on context, and always look back to ensure the rounded value appropriately represents the original calculation's result.