Question

Convert the following weights in pounds to kilograms (round to the nearest tenth where indicated). $81\mathrm{lb}=$ _______ $\mathrm{kg}$

Short answer

81 pounds is approximately 36.7 kilograms.

Step-by-step solution

Understand the Conversion Factor

To convert pounds to kilograms, we use the conversion factor: 1 pound is approximately equal to 0.453592 kilograms. This factor will be essential in converting the given weight from pounds to kilograms.

Set Up the Equation

We have 81 pounds that needs to be converted to kilograms. Using the conversion factor from Step 1, we can set up the equation as follows:$$81\text{ lb}\times 0.453592\text{ kg/lb}=x\text{ kg}$$

Perform the Multiplication

Carry out the multiplication to convert the weight from pounds to kilograms. Substitute into the equation:$$x=81\times 0.453592$$Calculating this, we get approximately 36.741 \text{ kg}.

Round the Result

The problem asks to round the result to the nearest tenth. The number 36.741 can be rounded to the nearest tenth as 36.7 kg, because the first number after the decimal (7) influences the tenths position.

Key concepts

Understanding Pounds to Kilograms Conversion

When converting weights from pounds to kilograms, you are transitioning between two different units of measurement. Pounds (lbs) are part of the imperial system, often used in the United States, while kilograms (kg) belong to the metric system, used worldwide.
To perform this conversion, it's essential to know a reliable conversion factor that relates the two units. By applying this conversion factor, you seamlessly translate a value expressed in pounds into its equivalent in kilograms. This method is useful not only in academics but also in real-life scenarios such as health, fitness, and science. Understanding this concept helps you move efficiently between different measurement standards.

The Role of the Conversion Factor

The conversion factor is a constant you multiply by to change one unit of measurement into another. In this problem, the pivotal conversion factor is that 1 pound is approximately equal to 0.453592 kilograms. This number is crucial because it translates measurements from pounds to kilograms.
To apply the conversion factor, use a straightforward multiplication:

• Identify the number of pounds you want to convert.
• Multiply this number by 0.453592 kg/lb to find the equivalent in kilograms.

This relationship serves as a bridge between the two different measurement systems, ensuring accuracy in conversions. Consistency when using the conversion factor guarantees that your results are reliable for all your calculations.

The Importance of Rounding Numbers

Rounding numbers is a useful mathematical skill that helps simplify lengthy numbers, making them easier to understand and use in practical situations. In weight conversions, this is particularly helpful for expressing measurements with a reasonable degree of precision.
In the given exercise, the calculated weight in kilograms was 36.741. To round, focus on the first decimal place (tenths). Here, we have 36.741, and the number immediately after the tenths place, which is 4, helps decide how to round.

• If this number is 5 or greater, increase the tenths place by one.
• If it is less than 5, leave the tenths place unchanged.

After rounding, the weight becomes 36.7 kg. Being able to round gives your answer clarity and maintains appropriate levels of accuracy needed for most real-world applications.