Question

Convert the following to the equivalent measures indicated. \(75 \mathrm{lb}=\) ______ \(\mathrm{kg}\)

Short answer

75 lb is approximately 34.02 kg.

Step-by-step solution

Understand the Conversion Factor

To convert pounds (lb) to kilograms (kg), we use the conversion factor: 1 lb = 0.45359237 kg.

Set Up the Conversion Equation

Write the equation using the conversion factor: \(75 \text{ lb} \times \frac{0.45359237 \text{ kg}}{1 \text{ lb}}\)

Perform the Calculation

Multiply 75 by 0.45359237 to convert pounds to kilograms: \(75 \times 0.45359237 = 34.01942775\text{ kg}\)

Round the Result

Round the result to a reasonable number of significant figures. Here, we round to two decimal places: \(34.02 \text{ kg}\)

Key concepts

Mathematical Calculations

Mathematical calculations form the backbone of unit conversion. When converting units, a mathematical equation will help change one measure to another. Here we needed to convert 75 pounds to kilograms.

The magic truly starts when you set up the problem using what you know about both units. For pounds and kilograms, we learned from the given conversion factor that 1 pound equals 0.45359237 kilograms. This conversion factor is crucial in creating a mathematical setup: multiply the number of pounds by this factor.

• The mathematical equation freezes out confusion and ensures accuracy.
• When you multiply 75 by 0.45359237, you calculate the equivalent weight in kilograms.
• Understanding this step is critical for accurate conversions in various units.

Conversion Factors

Conversion factors are essential numbers that relate one unit to another. They act like a bridge that helps navigate from one type of measurement to another easily.

In our problem, going from pounds to kilograms required the conversion factor: 1 lb = 0.45359237 kg. Without this factor, converting between the two measurements would seem like an impossible task. Here’s what to remember:

• They allow for conversion by providing a consistent relation.
• Multiply the current measurement by the conversion factor to find the equivalent in the desired unit.
• Choosing the correct factor is essential for accuracy and understanding.

Using the right conversion factor guarantees that your outcome is both reliable and valid in any conversion task.

Significant Figures

Significant figures help indicate the precision of a measurement in any mathematical task. They show how precise a calculation is by communicating the certainty of the numbers used.

When performing unit conversions like converting pounds to kilograms, it’s important to pay attention to significant figures to ensure that your final result reflects the precision level of your initial data.

• After the calculation, look at the initial value's number of significant figures.
• Round the final result to match the precision of your starting measurement.

In this exercise, we rounded the calculation 34.01942775 kg to 34.02 kg. This convention not only provides a clear result but also maintains the mathematical and scientific precision necessary for proper communication.