Question

Change \(7,000\) pounds to tons. A. \(14,000 \mathrm{t}\) B. \(7 t\) C. \(10 \mathrm{t}\) D. \(3.5 \mathrm{t}\)

Short answer

7,000 pounds is equal to 3.5 tons, so the answer is D.

Step-by-step solution

Understanding the Conversion Factor

To convert pounds to tons, we need to know how many pounds are in a ton. There are 2,000 pounds in one ton.

Setting Up the Conversion

We need to divide the number of pounds we have by the number of pounds in a ton. So for 7,000 pounds, we use the expression: \[ \frac{7,000 \text{ pounds}}{2,000 \text{ pounds per ton}} \]

Performing the Calculation

Now we need to perform the division: \[ \frac{7,000}{2,000} = 3.5 \] This means 7,000 pounds is equal to 3.5 tons.

Matching the Answer to the Options

From the options given: A. 14,000 t, B. 7 t, C. 10 t, D. 3.5 t, we see that the correct conversion 3.5 tons matches option D.

Key concepts

Pounds to Tons Conversion

When you need to convert a quantity from pounds to tons, it all starts with knowing the relationship between these two units. This is essential for problems dealing with heavy weights, like industrial shipments or large equipment. Understanding this conversion can help in various real-life situations. A ton is a larger unit used to measure weight, particularly in the United States, and it simplifies expressing large numbers of pounds.
1 ton equals 2,000 pounds, so when converting pounds to tons, the main step involves using this relationship to make the calculations. This conversion helps in reducing large numbers and making them more manageable.

Conversion Factor

Every conversion problem rests on a key element: the conversion factor. A conversion factor is a numerical value used to convert one unit into another and is crucial for accurately transitioning between measurements.
For our exercise, the conversion factor between pounds and tons is 2,000. This means 2,000 pounds is equivalent to one ton.

• If you know how many pounds you have, divide by 2,000 to convert pounds to tons.
• Conversely, to convert tons back to pounds, multiply the number of tons by 2,000.

Understanding and correctly applying the conversion factor allows you to effectively solve unit conversion problems.

Mathematical Calculation

Once you understand the conversion factor, the next step is the mathematical calculation. This involves straightforward division, a basic arithmetic operation. By dividing the total number of pounds by 2,000, you can calculate the equivalent in tons.
In our example, we have: \[ \frac{7,000}{2,000} = 3.5 \] This tells us that 7,000 pounds is 3.5 tons. The key is to ensure accuracy in this division, as even small errors can lead to incorrect conversions. Always double-check your division to confirm the results, ensuring the decimal placement is correct, leading to accurate problem-solving.

Problem-Solving Steps

Understanding step-by-step problem-solving is vital for tackling math exercises confidently. Let's briefly go over these steps again for clarity:

• **Identify the Units:** Recognize you are converting pounds to tons.
• **Know the Conversion Factor:** Remember that 2,000 pounds equals one ton.
• **Perform the Calculation:** Divide 7,000 by 2,000 to find the answer.
• **Match Your Answer:** Compare your result to given options, confirming that 3.5 tons aligns with option D.

Following these steps helps in systematically solving similar problems, reducing errors and enhancing understanding of unit conversions.