Question

Convert the following weights to kilograms. (Round to the nearest tenth.) \(9 \mathrm{lb}, 3 \mathrm{oz}=\) _______ \(\mathrm{kg}\)

Short answer

4.2 kg

Step-by-step solution

Understand the Conversion Rates

To solve this exercise, we need to convert pounds and ounces to kilograms. The conversion rates are as follows: - 1 pound (lb) = 0.453592 kilograms (kg) - 1 ounce (oz) = 0.0283495 kilograms (kg).

Convert Pounds to Kilograms

First, convert the 9 pounds to kilograms using the conversion rate for pounds to kilograms.Calculation: \[ 9 \text{ lb} = 9 \times 0.453592 \text{ kg/lb} = 4.082328 \text{ kg} \]

Convert Ounces to Kilograms

Next, convert the 3 ounces to kilograms using the conversion rate for ounces to kilograms.Calculation: \[ 3 \text{ oz} = 3 \times 0.0283495 \text{ kg/oz} = 0.0850485 \text{ kg} \]

Sum the Kilograms

Add the kilograms obtained from the pounds and the ounces to get the total weight in kilograms.Calculation: \[ 4.082328 \text{ kg} + 0.0850485 \text{ kg} = 4.1673765 \text{ kg} \]

Round to Nearest Tenth

Finally, round the total kilograms to the nearest tenth.Rounded Total: \[ 4.1673765 \text{ kg} \approx 4.2 \text{ kg} \]

Key concepts

Understanding Kilograms

Kilograms are a base unit of mass in the International System of Units (SI). It is commonly used worldwide and provides a standard measurement for both scientific and everyday use. One kilogram is roughly equivalent to the mass of one liter of water. This makes it a convenient unit for measuring everything from body weight to grocery items.

• Symbol: kg
• Commonly used in science, industry, and health.
• Integral part of the metric system.

The kilogram is advantageous because it uses the decimal system, which simplifies calculations, especially when converting to other metric units like grams or tonnes. For instance, 1000 grams equals 1 kilogram, which is easy for anyone to compute.

Converting Pounds to Kilograms

The process of converting pounds to kilograms involves using a specific conversion factor. For every pound, there are approximately 0.453592 kilograms. When you need to change pounds to kilograms, simply multiply the number of pounds by this conversion factor.
For example, let's convert 9 pounds to kilograms:

• Calculation: \( 9 \text{ lb} \times 0.453592 \text{ kg/lb} = 4.082328 \text{ kg} \)

This calculation highlights the importance of knowing and applying the appropriate conversion factor to obtain the correct result. Rounding may be necessary, based on the precision required.

Converting Ounces to Kilograms

Converting ounces to kilograms is similar to the pound-to-kilogram process but uses a different conversion factor. One ounce is equivalent to about 0.0283495 kilograms.
This step is crucial when dealing with small weights such as baking ingredients or postal items.

• For example, converting 3 ounces to kilograms involves:\( 3 \text{ oz} \times 0.0283495 \text{ kg/oz} = 0.0850485 \text{ kg} \).

This emphasizes the need for accurate calculations, particularly with lower weight measurements, where even minor errors can significantly affect the outcome.

General Weight Conversion Tips

Weight conversion can be simple if you understand and apply the correct formulas. Here are some general tips:

• Always have conversion factors handy, like 1 lb = 0.453592 kg and 1 oz = 0.0283495 kg.
• Double-check calculations, particularly in scientific and commercial settings where accuracy is important.
• Be mindful of units and ensure consistency throughout calculations.
• When rounding, consider the level of precision required by the context.

By mastering these tips, converting between different weight units becomes a straightforward task.

The Role of Mathematics Education in Weight Conversion

Mathematics education equips students with essential skills like unit conversion, which are applicable in various real-life scenarios. Whether tackling weight conversion problems or dealing with financial transactions, math provides the tools to solve practical issues.

• It builds a strong foundation for scientific understanding and technological development.
• Encourages logical thinking and problem-solving abilities.
• Contributes to improved computational skills and numerical literacy.

Ultimately, a solid math education helps students become confident in handling units and measurements, which are crucial in everyday life and numerous professions.