Question

The Star of Africa, a diamond in the royal scepter of the British crown jewels, has a mass of \(530.2\) carats, where 1 carat \(=0.20 \mathrm{~g}\). Given that \(1 \mathrm{~kg}\) has a weight of \(2.21 \mathrm{lb}\), what is the weight of the Star of Africa in pounds?

Short answer

The weight of the Star of Africa is approximately 0.23 pounds.

Step-by-step solution

Understand the Conversion Factors

First, identify the conversion factors we need to use to solve this problem. We know that 1 carat equals 0.20 grams and 1 kilogram is equivalent to 2.21 pounds.

Convert Carats to Grams

Use the conversion factor to convert the mass of the diamond from carats to grams.Given mass = 530.2 carats, and 1 carat = 0.20 grams, the calculation is:\[mass\ in\ grams = 530.2 \times 0.20 = 106.04\ grams\]

Convert Grams to Kilograms

Convert the mass from grams to kilograms since our conversion factor for pounds involves kilograms.\[mass\ in\ kilograms = \frac{106.04}{1000} = 0.10604\ kilograms\]

Convert Kilograms to Pounds

Finally, convert the mass from kilograms to pounds using the conversion factor that 1 kg = 2.21 lbs.\[mass\ in\ pounds = 0.10604 \times 2.21 = 0.2343284\ pounds\]

Round the Result

Round the result to an appropriate number of decimal places (typically two places for pound conversions).\[mass\ in\ pounds = 0.23\ pounds\]

Key concepts

Mass Conversion

Mass conversion is the process of converting one unit of mass into another. It’s a crucial skill in science and commerce, such as when you buy groceries or measure ingredients for a recipe. Let's dive deeper into understanding mass conversion.

When converting mass, you'll often start with a given unit, like carats, cups, or grams, and shift it to your desired unit. For example, to find out the mass of the Star of Africa diamond in grams, you begin with its mass in carats and use the given conversion factor.

• Start with the initial mass: 530.2 carats.
• Use the conversion factor, where 1 carat = 0.20 grams.
• Multiply: 530.2 carats × 0.20 grams per carat = 106.04 grams.

This straightforward multiplication helps you accurately convert the mass into the unit needed for further calculations. Remember to keep track of your units to avoid any confusion during conversions.

Metric to Imperial Conversion

Metric to Imperial conversions involve changing units from the metric system, like grams and kilograms, to the Imperial system, such as pounds and ounces. This is useful because different regions around the world use different measurement systems.

For our exercise, we need to convert the mass of a diamond from the metric system to the Imperial system. First, you convert grams to kilograms:

• Given mass in grams: 106.04 grams.
• Convert to kilograms by dividing by 1000: \( rac{106.04}{1000} = 0.10604 \) kilograms.

Now, to convert kilograms to pounds by using the given conversion factor:

• Use the conversion factor, where 1 kg = 2.21 lbs.
• Multiply: 0.10604 kg × 2.21 lbs per kg = 0.2343284 lbs.

Understanding these conversions is essential for anyone dealing with international transactions or scientific research, where units might differ based on the audience or region.

Weight Calculation

Weight calculation involves using known conversion factors to determine how heavy an object is in a particular unit. In this case, after finding the mass of an object in grams or kilograms, we want to present it in pounds.

Calculating the weight in pounds can be done using simple math once we have the mass in kilograms. From previous calculations, we know:

• Mass in kilograms = 0.10604.
• Using the conversion: 0.10604 kg × 2.21 lbs per kg.
• The result gives the weight in pounds: 0.2343284 lbs.

Always remember to round off your final answer to a practical number of decimal places, which is generally two for pounds: 0.23 lbs. Rounding helps provide a clearer and more comprehensible result for real-life applications. This ensures the calculation is precise, practical, and easy to understand for everyone involved.