Question

Change 4 tons to ounces. A. \(128,000\) oz B. \(8,000\) oz C. \(80,000\) oz D. \(12,800\) oz

Short answer

The correct answer is A. 128,000 oz.

Step-by-step solution

Understand the Conversion Problem

We need to convert 4 tons into ounces. To do this, we need to know the conversion factors from tons to pounds, and then from pounds to ounces.

Convert Tons to Pounds

First, convert tons to pounds. We know that 1 ton equals 2,000 pounds. Therefore, if we have 4 tons, we multiply by 2,000 to find the number of pounds: \[ 4 \text{ tons} \times 2,000 \frac{\text{pounds}}{\text{ton}} = 8,000 \text{ pounds} \]

Convert Pounds to Ounces

Next, convert the pounds to ounces. We know that 1 pound equals 16 ounces. Therefore, using the 8,000 pounds calculated in the previous step, we multiply by 16 to find the number of ounces:\[ 8,000 \text{ pounds} \times 16 \frac{\text{ounces}}{\text{pound}} = 128,000 \text{ ounces} \]

Determine the Correct Answer Option

Finally, compare the total ounces calculated to the given options. The answer that matches our calculation is option A, 128,000 ounces.

Key concepts

Weights and Measures

Weights and measures are systems used to quantify physical quantities like weight, volume, and length. Understanding these measurements is crucial in many real-life scenarios, from cooking recipes to industrial production. For weight, the common units include ounces, pounds, and tons. Ounces are a smaller unit, often used in everyday items like food packaging. Pounds are larger, frequently used for items like groceries or luggage, while tons measure even heftier items like vehicles or massive machinery.
It is important to know the relationships between these units for correct conversions. For example, in the standard U.S. system:

• 1 pound = 16 ounces
• 1 ton = 2,000 pounds

With these equivalences, you can seamlessly switch between different units depending on the context of the problem or task.

Conversion Factors

A conversion factor is a numerical value used to convert one unit of measure to another. These factors are derived from equalities between different units. For instance, from the context of weight, we have:

• 1 ton = 2,000 pounds, so the conversion factor is 2,000 pounds per ton
• 1 pound = 16 ounces, translating into a conversion factor of 16 ounces per pound

Utilizing conversion factors correctly is essential in transforming quantities across various units. It ensures precision and consistency across measurements. The key is to ensure that the units you wish to cancel out are correctly aligned in your mathematical operation, a concept often applied in scientific fields and everyday mathematics.

Problem Solving

Problem solving in unit conversion involves a structured process to ensure you arrive at the correct result. First, identify the starting and required units, like converting tons to ounces in this case. Next, gather the conversion factors you need. This ensures you have the tools to convert through intermediate steps (e.g., tons to pounds, then pounds to ounces).
Break the problem into manageable steps:

• Convert starting units to an intermediate unit.
• Use another factor to reach the final desired unit.
• Check your work by verifying the final unit and the plausibility of the result.

Such breakdowns and systematic approaches are applicable across various math and science problems, enhancing accuracy and understanding.

Mathematical Operations

Mathematical operations are the backbone of unit conversions. They involve multiplying or dividing quantities based on the conversion factors. In the exercise provided, we used multiplication:

• For converting tons to pounds: multiply the amount of tons by 2,000 to switch to pounds.
• For converting pounds to ounces: multiply the resulting pounds by 16 to switch to ounces.

Each step ensures the problem transitions smoothly between units using clear calculations. Here, the solutions signify the importance of precise multiplying. Mistakes often occur if operations or conversion factors are applied incorrectly. Hence, understanding these mathematical principles helps avoid errors, ensuring accurate and meaningful results in conversions.