Textbook Question
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?
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2. Measurement and Problem Solving
Dimensional Analysis
1:47 minutesProblem 121
Textbook Question
a. An athlete with a body mass of 65 kg has 3.0% body fat. How many pounds of body fat does that person have? (2.6)
Verified step by step guidance1
Convert the body mass from kilograms to pounds using the conversion factor: 1 kg = 2.20462 pounds.
Calculate the total body mass in pounds by multiplying the body mass in kilograms by the conversion factor.
Determine the mass of body fat in pounds by calculating 3.0% of the total body mass in pounds.
Use the formula: \( \text{Body Fat (pounds)} = \text{Total Body Mass (pounds)} \times \frac{3.0}{100} \).
Ensure the units are consistent and verify the calculation steps for accuracy.
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1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Body Mass and Body Fat Percentage
Body mass refers to the total weight of an individual, typically measured in kilograms or pounds. Body fat percentage indicates the proportion of fat in relation to total body mass. In this case, the athlete's body fat percentage is 3.0%, meaning that 3.0% of their total body mass is composed of fat.
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Unit Conversion
Unit conversion is the process of converting a measurement from one unit to another. In this question, the athlete's body mass is given in kilograms, but the answer requires the body fat to be expressed in pounds. Understanding how to convert kilograms to pounds (1 kg = 2.20462 lbs) is essential for accurately calculating the amount of body fat.
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Calculating Body Fat
To calculate the amount of body fat, one must multiply the total body mass by the body fat percentage (expressed as a decimal). For example, if an athlete weighs 65 kg and has 3.0% body fat, the calculation involves finding 3.0% of 65 kg, which gives the total mass of body fat in kilograms before converting it to pounds.
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