Question

Change \(12,800\) pounds to tons. A. \(6.4 \mathrm{T}\) B. \(640 T\) C. \(64 \mathrm{T}\) D. \(6 T\)

Short answer

The correct answer is A: 6.4 T.

Step-by-step solution

Understand the Units

To solve the problem, we need to convert pounds to tons. In weight measurements, there are two commonly used ton units: a short ton and a long ton. A short ton is equivalent to 2,000 pounds in the United States customary system. For this problem, assuming the short ton is used.

Set Up the Conversion

We know from Step 1 that 1 ton is equal to 2,000 pounds. So we can set up a conversion factor to convert 12,800 pounds to tons. The conversion factor will be \( \frac{1 \, \text{ton}}{2,000 \, \text{pounds}} \).

Perform the Calculation

To perform the conversion, multiply 12,800 pounds by the conversion factor:\[ 12,800 \, \text{pounds} \times \frac{1 \, \text{ton}}{2,000 \, \text{pounds}} = 6.4 \, \text{tons} \]

Determine the Correct Answer

From the calculation, we have found that 12,800 pounds is equal to 6.4 tons. Comparing this with the given options, A. \(6.4 \mathrm{T}\) is the correct answer.

Key concepts

Weight Measurement

Understanding weight measurement is essential for converting between different units. Weight is a measure of the force exerted by gravity on an object. It's often confused with mass, but they are different concepts. Weight is typically measured using scales and is expressed in units such as pounds, kilograms, grams, or tons.

Units of weight are part of two primary measuring systems: the metric system, which includes grams and kilograms, and the customary (imperial) system, commonly used in the United States, which includes pounds and tons.

• Pounds: A pound is a unit of weight in the customary system equal to 16 ounces.
• Tons: In the customary system, there are two types of tons: short ton and long ton, which are applicable in different contexts.

Understanding these basic concepts is crucial when tackling unit conversions in weight measurement.

Short Ton

The short ton is a unit of weight primarily used in the United States. It's part of the customary system and is often used for larger quantities, like shipping or selling bulk goods.

Here are some important attributes of the short ton:

• Weight Equivalent: One short ton equals 2,000 pounds. This relationship is crucial when converting between pounds and tons.
• Applications: Short tons are used especially in industries such as construction, mining, and agriculture where bulk materials like coal, rocks, and grains are prevalent.

When doing conversions, always be clear on whether you're using short tons or some other version of tons, like the metric or long ton.

Long Ton

The long ton is another unit of weight used predominantly in the United Kingdom. It differs from the short ton and is a part of the British imperial system, which has a significant history alongside the United States customary system.

Key information about the long ton includes:

• Weight Equivalent: One long ton is equivalent to 2,240 pounds. This makes it heavier than a short ton.
• Usage: Long tons are commonly used in shipping and some British industries, like in older naval contexts for vessels and bulk materials.

Since long tons differ from short tons, it's vital to know which unit you are working with when converting weights.

Conversion Factor

A conversion factor allows you to change numbers from one unit to another while ensuring accuracy and equivalency. It plays a pivotal role in unit conversions.

For conversion between pounds and tons, a reliable factor is essential.

• Basics: A conversion factor is essentially a fraction or ratio that equals one. For example, when converting pounds to short tons, the factor is \( \frac{1 \, \text{ton}}{2,000 \, \text{pounds}} \).
• Application: To perform a conversion, multiply the amount in the original unit (like pounds) by the conversion factor, ensuring that units correctly cancel out. For example: \( 12,800 \, \text{pounds} \times \frac{1 \, \text{ton}}{2,000 \, \text{pounds}} = 6.4 \, \text{tons} \).

Employing the correct conversion factor is crucial for accurate unit transformations in mathematical and real-world contexts.