Gemstones are weighed in carats, with 1 carat =200 mg (exactly). What is the mass in grams of th

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Gemstones are weighed in carats, with 1 carat =200 mg...

Gemstones are weighed in carats, with 1 carat $=200 \mathrm{mg}$ (exactly). What is the mass in grams of the Hope Diamond, the world's largest blue diamond at $44.4$ carats? What is this mass in ounces? (See conversion on the inside back cover.)

Key Concepts

Dimensional Analysis

Dimensional analysis is a systematic method to convert one kind of unit to another by multiplying by conversion factors that cancel out unwanted units. This technique not only helps ensure the correct final units but also checks that the computation is set up logically and accurately.

Imperial Units (Ounces)

Ounces are a unit of mass used primarily in the United States and other countries using the imperial system. Converting from metric units like grams to ounces typically involves using a fixed conversion factor, which facilitates understanding and comparing measurements across different unit systems.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another, using a conversion factor. It is a fundamental skill in many areas of science and mathematics, allowing quantities measured in different systems to be accurately compared or combined.

Carat as a Unit of Mass

A carat is a unit commonly used to measure the mass of gemstones. It is defined exactly as 200 milligrams, making it a standardized measure in the jewelry industry. Understanding this unit is crucial for accurately converting the weight of gemstones into other mass units.

Metric Units and Conversions

Metric units such as milligrams and grams are based on powers of ten, making conversions between them straightforward. Since 1 gram equals 1,000 milligrams, converting a mass given in milligrams to grams involves dividing by 1,000, a concept central to many scientific computations.

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