Question

The weight of a diamond is measured in carats. How many pounds does a \(5.75\)-carat diamond weigh? ( 1 carat \(=200\). mg)

Short answer

0.00253 pounds

Step-by-step solution

Convert carats to milligrams

First, find the weight of the diamond in milligrams. Given that 1 carat equals 200 milligrams, multiply the carat weight by 200. So, the calculation is: \(5.75 \text{ carats} \times 200 \text{ mg per carat} = 1150 \text{ mg}\)

Convert milligrams to grams

Next, convert the weight from milligrams to grams. Since 1 gram equals 1000 milligrams, divide by 1000.\(1150 \text{ mg} \times \frac{1 \text{ gram}}{1000 \text{ mg}} = 1.15 \text{ grams}\)

Convert grams to pounds

Finally, convert the weight from grams to pounds. Since 1 pound equals 453.592 grams, divide the gram weight by 453.592.\(1.15 \text{ grams} \times \frac{1 \text{ pound}}{453.592 \text{ grams}} \ \approx 0.00253 \text{ pounds}\)

Key concepts

carats to milligrams

Understanding how to convert carats to milligrams in chemistry is key, especially when dealing with precious stones like diamonds. A carat is a unit of mass used for gemstones, and it equals 200 milligrams. To perform the conversion, simply multiply the carat value by 200. For example, a diamond weighing 5.75 carats is calculated as follows: \(5.75 \text{ carats} \times 200 \text{ mg/carats} = 1150 \text{ milligrams}\) This step helps us understand how much the diamond weighs in milligrams, a more commonly used unit in chemistry than carats. By knowing the carat-to-milligram conversion, we make it easier to transition to other units, preparing us for more complex calculations.

milligrams to grams

After converting carats to milligrams, the next logical step is converting milligrams to grams. This is important because grams are a standard scientific unit of mass. The conversion factor here is straightforward: 1 gram equals 1000 milligrams. To convert, you divide the number of milligrams by 1000: \(1150 \text{ milligrams} \times \frac{1 \text{ gram}}{1000 \text{ milligrams}} = 1.15 \text{ grams}\) This conversion helps make further calculations simpler. It's easier to work with grams when dealing with larger masses in scientific scenarios. Being comfortable with converting between milligrams and grams is an essential skill for any chemistry student.

grams to pounds

The final step in our unit conversion exercise is to convert grams to pounds. Pounds are commonly used in everyday life in the United States, so understanding this conversion is quite practical. Since 1 pound equals 453.592 grams, you convert grams to pounds by dividing by this number. For example: \(1.15 \text{ grams} \times \frac{1 \text{ pound}}{453.592 \text{ grams}} \approx 0.00253 \text{ pounds}\) This final step shows how a unit you started in carats can end up in a familiar unit like pounds. Knowing how to make these conversions can help you solve real-world problems and is a useful skill beyond chemistry. Understanding each step allows you to tackle more complex unit conversions with confidence.