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Ch.1 Matter and Measurements
McMurry - Fundamentals of GOB 8th Edition
McMurry8th EditionFundamentals of GOBISBN: 9780134015187Not the one you use?Change textbook
Chapter 1, Problem 95

Gemstones are weighed in carats, where 1 carat = 200 mg exactly. What is the mass in grams of the Hope diamond, the world's largest blue diamond, at 44.4 carats?

Verified step by step guidance
1
Step 1: Understand the relationship between carats and milligrams. The problem states that 1 carat is equal to 200 milligrams (mg).
Step 2: Write the given information. The mass of the Hope diamond is 44.4 carats.
Step 3: Set up a conversion factor to convert carats to milligrams. Use the relationship: \( 1 \text{ carat} = 200 \text{ mg} \). Multiply the given carats by this conversion factor.
Step 4: Convert the result from milligrams to grams. Use the relationship: \( 1 \text{ g} = 1000 \text{ mg} \). Divide the mass in milligrams by 1000 to get the mass in grams.
Step 5: Combine the steps into a single calculation: \( \text{Mass in grams} = 44.4 \text{ carats} \times \frac{200 \text{ mg}}{1 \text{ carat}} \times \frac{1 \text{ g}}{1000 \text{ mg}} \). Simplify the expression to find the final mass in grams.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Carat Measurement

A carat is a unit of weight used for gemstones and pearls, where one carat is equivalent to 200 milligrams. This measurement is crucial in the jewelry industry as it helps determine the value and size of gemstones. Understanding carats is essential for converting gemstone weights into grams or other units.
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Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to another unit. In this context, converting carats to grams involves using the conversion factor that 1 carat equals 0.2 grams. Mastery of unit conversion is vital for accurately calculating weights and understanding measurements in different contexts.
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Mass and Weight

Mass refers to the amount of matter in an object, typically measured in grams or kilograms, while weight is the force exerted by gravity on that mass. In this question, we focus on mass, as we are converting the weight of the Hope diamond from carats to grams. Recognizing the distinction between mass and weight is important in scientific calculations.
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