Question

Convert the following weights to kilograms. (Round to the nearest tenth.) \(5 \mathrm{lb}, 5 \mathrm{oz}=\) _______ \(\mathrm{kg}\)

Short answer

5 lb, 5 oz is approximately 2.4 kg.

Step-by-step solution

Understand the question

We need to convert a weight given in pounds and ounces (5 lb, 5 oz) into kilograms and round the result to the nearest tenth.

Convert pounds to kilograms

We know that 1 pound is approximately 0.453592 kilograms. Therefore, to convert 5 pounds to kilograms, we multiply:\[5 \text{ lb} \times 0.453592 \text{ kg/lb} = 2.26796 \text{ kg}\]

Convert ounces to kilograms

There are 16 ounces in a pound, and therefore 1 ounce is \(\frac{1}{16}\) of a pound. Convert 5 ounces to pounds first:\[5 \text{ oz} \times \frac{1}{16} \text{ lb/oz} = 0.3125 \text{ lb}\]Then, convert 0.3125 pounds to kilograms:\[0.3125 \text{ lb} \times 0.453592 \text{ kg/lb} = 0.141747 \text{ kg}\]

Add converted kilograms

Add the weight in kilograms from the pounds conversion and the ounces conversion to get the total weight in kilograms:\[2.26796 \text{ kg} + 0.141747 \text{ kg} = 2.409707 \text{ kg}\]

Round to the nearest tenth

The number 2.409707 to the nearest tenth is 2.4. Therefore, the weight in kilograms rounded to the nearest tenth is 2.4 kg.

Key concepts

Understanding the Metric System

The metric system is a decimal-based system of measurement used by most countries around the world. It is designed to be simple and easy to use, with units that scale by powers of ten. This system includes units such as meters for length, liters for volume, and grams for mass. Unlike other measurement systems that might use varied units for the same type of measurement, the metric system ensures consistency by using prefixes like milli-, centi-, and kilo- to indicate subdivisions or multiples of the base unit. For example, 1 kilogram equals 1,000 grams, demonstrating the simplicity and scalability inherent in the metric system.

By standardizing measurements globally, the metric system facilitates easier communication and conversion of measurements. This consistency is particularly useful in scientific contexts and international commerce, where precise and easily understood measurements are critical.

Simplifying Unit Conversion

Unit conversion is the process of changing a measurement from one unit to another, especially when moving between different measurement systems. In the case of converting weights from pounds and ounces to kilograms, understanding the relationships between these units is crucial. Conversion involves using conversion factors, which are numerical values that express the relationship between the units.

For instance, since 1 pound approximately equals 0.453592 kilograms, this conversion factor can be used to translate weights between these two units. Similarly, understanding that there are 16 ounces in a pound allows us to perform conversions in a two-step process—first converting ounces to pounds, then converting the total weight to kilograms. This methodical approach ensures accuracy in conversion and helps in visualizing how different units relate to one another.

The Significance of Kilograms in Measuring Mass

Kilograms are the base unit of mass in the metric system and are widely used in both everyday and scientific contexts. The kilogram's advantage lies in its alignment with the metric system's decimal structure, facilitating easy calculation and comprehension.

In various applications, from weighing groceries to scientific experiments, using kilograms simplifies the process of standardizing mass measurements. Because the kilogram is part of the metric system, it pairs easily with other metric units, enabling seamless conversions and calculations.

When converting from non-metric units like pounds, recognizing that each pound corresponds to about 0.453592 kilograms is key. This allows for straightforward and accurate conversions, making kilograms an effective unit for global mass measurement.

Converting Pounds and Ounces to Kilograms

Converting weights from pounds and ounces to kilograms involves breaking down the process into two parts. First, you need to convert pounds to kilograms. Since 1 pound is equal to approximately 0.453592 kilograms, you simply multiply the number of pounds by this conversion factor.

Next, you tackle the ounces. Remember that 1 pound equals 16 ounces, so you divide the number of ounces by 16 to convert them to pounds. Once converted to pounds, you use the same conversion factor (0.453592) to convert the weight into kilograms.

Finally, you add the kilograms from both conversions to get the total weight in kilograms and round to the nearest tenth, if necessary. This multi-step conversion process might seem intricate at first, but breaking it down simplifies the task and ensures accuracy. Understanding how to perform these conversions can help you comfortably interchange between various weight measurement systems.