Problem 141 - General Chemistry

Question

The masses of diamonds and gems are measured in carats. A carat is defined as \(200 \mathrm{mg}\). If a jeweler has 384 carats of diamonds, how many grams does she have?

Step-by-Step Solution

Answer

384 carats is equivalent to 76.8 grams of diamonds.

Step 1: Understanding the Unit Conversion

First, we need to understand that the problem requires converting the mass from carats to grams. We know that 1 carat equals 200 milligrams.

Step 2: Converting Milligrams to Grams

To convert milligrams to grams, remember that there are 1000 milligrams in a gram. Therefore, to convert milligrams to grams, divide by 1000.

Step 3: Performing the Conversion

Multiply the number of carats by the milligram value of one carat to get the total milligrams. Then, convert this total to grams. Specifically, 384 carats multiplied by 200 mg per carat equals 76800 mg. Divide 76800 mg by 1000 to convert it to grams.

Step 4: Calculating the Final Answer

Continue from the previous step: \( \frac{76800 \text{ mg}}{1000} = 76.8 \text{ grams} \). Hence, 384 carats is equivalent to 76.8 grams.

Key Concepts

Carat to Gram Conversion

When dealing with precious stones, like diamonds, carat is the standard unit of mass. Understanding this conversion is crucial if you're working with gemstones.

• Carat Definition: A carat is defined as 200 milligrams ( \(200 ext{ mg} \)).
• Conversion Importance: Knowing how to convert carats to grams simplifies the trading and evaluation processes in gemology.

To convert carats to grams, first convert the carats to milligrams. For example, if you have 384 carats, each carat equals 200 milligrams, so multiply 384 carats by 200 milligrams per carat. This equals 76800 milligrams. Performing this conversion helps you to understand the weight of gemstones in a more familiar unit of measure, like grams. This conversion process becomes straightforward once you remember the relationship between carats, milligrams, and grams.

Mass Measurement

Mass measurement often involves determining the amount of matter in an object. Different units are used depending on the size and type of material being measured. In scientific contexts, milligrams, grams, and kilograms are commonly used.

• Understanding Mass: Mass is a fundamental property of physical bodies and is a measure of the amount of matter contained in an object.
• Units of Mass: Common units include milligrams (mg), grams (g), and kilograms (kg).

When working with smaller units like milligrams, understanding the need for accurate and precise conversion methods is essential. This knowledge ensures consistency whether you are measuring small objects like gemstones or calculating dosages in pharmaceuticals.

Milligram to Gram Conversion

Converting milligrams to grams is a basic yet crucial skill when dealing with small-scale measurements.

• Basic Concept: The key to this conversion is knowing that 1 gram equals 1000 milligrams.
• Conversion Process: To convert milligrams to grams, divide the milligram quantity by 1000.

For instance, if you have 76800 milligrams, converting this to grams involves dividing by 1000, resulting in 76.8 grams. Remember, dividing by 1000 is equivalent to shifting the decimal point three places to the left. This method is handy when working with scientific calculations, nutritional facts, or jewel evaluations, as it provides a clearer perspective on the item's weight.