Question

Convert the following weights in kilograms to pounds (round to the nearest tenth of a pound). A client weighs \(99.2 \mathrm{~kg} .\) How many pounds does the client weigh? (Round to the nearest tenth.) _______ \(\mathrm{lb}\)

Short answer

The client weighs 218.7 lb.

Step-by-step solution

Identify the Conversion Factor

To convert kilograms to pounds, we use the conversion factor 1 kilogram = 2.20462 pounds. This will help us transform the weight measurement from kilograms to pounds.

Set Up the Conversion Equation

Multiply the given weight in kilograms by the conversion factor. This means calculating \(99.2~\text{kg} \times 2.20462~\text{lb/kg}\).

Perform the Calculation

Carry out the multiplication: \(99.2 \times 2.20462 = 218.703184\). The result of this multiplication gives the weight in pounds before rounding.

Round the Result

Round the calculated weight to the nearest tenth of a pound. From \(218.703184\), we round to \(218.7\) since the digit in the hundredths place is 0, which means we round down.

Key concepts

Weights and Measures

Understanding weights and measures is crucial when dealing with unit conversions. Measurements of weight often use different units, depending on the region or context. For example, in many parts of the world, weight is commonly measured in kilograms (kg), while in the United States, pounds (lb) are more frequently used.
One reason to be familiar with these units is that certain sectors, like health and science, might require you to convert between them regularly. Knowing how to switch from kilograms to pounds and vice versa ensures accuracy and efficiency in your calculations. So, whenever you're faced with a weight conversion problem, understanding these basic units is the first step towards a solution.

Conversion Factor

The conversion factor is a crucial number that allows you to transform one unit of measurement to another.
When converting weights from kilograms to pounds, you'll use the conversion factor 1 kilogram = 2.20462 pounds. This number is essentially a bridge between the metric system and the imperial system and allows for straightforward calculations.

• Always ensure you're using the correct conversion factor for accurate results.
• Multiply the original measurement by the conversion factor to switch from one unit to another.

It's these precise calculations that allow fields like international trade, science, and even personal health management to function smoothly across different measurement systems.

Rounding Numbers

Rounding numbers is an essential step in ensuring that your final results are practical and easy to read. It simplifies numbers while still staying true to their value. When rounding, especially in unit conversions, you often need to follow particular rules.
For instance, we round to the nearest tenth when dealing with unit conversions in weights to make our numbers friendlier and easier to understand. In our example, the figure 218.703184 is rounded to 218.7. This simplification occurs because the digit in the hundredths place (0) suggests rounding down rather than up.

• Check the number directly after your desired decimal place to determine how to round.
• If that number is 0-4, you round down, and if 5-9, you round up.

Mathematical Calculations

Completing mathematical calculations correctly is key to solving unit conversion problems. Calculations typically involve multiplying a given number by a conversion factor, identifying precise results, and then rounding them appropriately.
In our exercise, we have the multiplication: \[99.2~\text{kg} \times 2.20462~\text{lb/kg} = 218.703184~\text{lb}\]
Once you perform these calculations, you're not quite finished until you manage the final results neatly, often through rounding.

• Carry out the multiplication first without worrying about rounding just yet.
• Remember that each step, from multiplying to rounding, ensures that all aspects of your problem are solved clearly and logically.

By keeping your calculations organized, students can improve their skills in precision and accuracy in math and science.