Question

Convert the following weights to kilograms. (Round to the nearest tenth.) \(10 \mathrm{lb}, 12 \mathrm{oz}=\) _______ \(\mathrm{kg}\)

Short answer

4.9 kg

Step-by-step solution

Convert Pounds to Kilograms

We know that 1 pound is approximately equal to 0.453592 kilograms. Since we have 10 pounds, the conversion to kilograms is: \[10 \times 0.453592 = 4.53592 \text{ kg}\]

Convert Ounces to Kilograms

There are 16 ounces in a pound, and 1 pound is equivalent to 0.453592 kilograms. First, convert 12 ounces to pounds: \[\frac{12}{16} = 0.75 \text{ pounds}\]Now, convert the 0.75 pounds to kilograms:\[0.75 \times 0.453592 = 0.340194 \text{ kg}\]

Add Kilograms from Pounds and Ounces

Add the kilograms obtained from both the pounds and ounces:\[4.53592 \text{ kg} + 0.340194 \text{ kg} = 4.876114 \text{ kg}\]

Round to the Nearest Tenth

Round the total kilogram weight to the nearest tenth:\[4.876114 \approx 4.9 \text{ kg}\]

Key concepts

Kilogram Conversion

Converting weights from pounds and ounces to kilograms is a common task in mathematics education, particularly when learning about unit conversion. The essence of kilogram conversion lies in using the known value that 1 pound is approximately 0.453592 kilograms.
To effectively perform kilogram conversion, you need to:

• Identify the total weight in pounds. For example, in our exercise, we start with 10 pounds.
• Calculate the corresponding kilograms by multiplying by 0.453592.

This approach allows easy transition between the Imperial system commonly used in the United States and the Metric system used in most other countries. Understanding the conversion factor is crucial for accurate mathematical calculations in real-world applications.

Rounding

Rounding is a fundamental concept in mathematics education, simplifying numbers to make them easier to work with or to meet specific measurement constraints. When we round to the nearest tenth, we focus on the first decimal place.
In our example, we arrived at a weight of 4.876114 kg after conversions. To round to the nearest tenth:

• Look at the second decimal place, which is 7 here.
• If this number is 5 or greater, round up the first decimal place by one. Otherwise, leave it as is.

Therefore, 4.876114 becomes 4.9. Rounding helps in reducing complexity while ensuring adequate precision for most practical purposes.

Unit Conversion

Unit conversion bridges the gap between different measurement systems. Whether dealing with length, weight, or volume, converting units helps to unify and simplify data exchange.
For weight, this often involves:

• Converting between pounds and ounces within the Imperial system.
• Switching between Imperial and Metric, such as converting pounds to kilograms.

Understanding unit conversion empowers students to navigate and apply mathematical knowledge to diverse scientific and everyday contexts. It’s vital to remember that consistency in units is key to accuracy in any mathematical operation.

Mathematics Education

Mathematics education encompasses a broad range of skills including numbers, operations, and problem-solving techniques like conversion and rounding. Educators aim to provide students with tools like unit conversion factors and rounding rules to solve practical problems.
In teaching these concepts:

• Kilogram conversion is taught early in conjunction with understanding basic mathematical functions like multiplication.
• Rounding is reinforced through exercises that illustrate its application in real scenarios like weight measurement.

The goal of mathematics education is to ensure the student feels comfortable with these processes, encouraging a deeper understanding of how mathematics integrates into everyday life and various scientific disciplines.