Problem 37 - Prealgebra

Question

A certain brand of vitamin C contains \(500 \mathrm{mg}\) per tablet. A bottle contains 240 tablets. How many total grams of vitamin \(\mathrm{C}\) are in this bottle?

Step-by-Step Solution

Answer

There are 120 grams of vitamin C in the bottle.

Step 1: Understand the Relationship Between Milligrams and Grams

Recall that 1 gram (g) is equal to 1000 milligrams (mg). This means to convert milligrams to grams, you need to divide by 1000.

Step 2: Calculate Milligrams of Vitamin C in the Entire Bottle

Each tablet contains 500 mg of vitamin C, and there are 240 tablets in the bottle. Multiply the amount of vitamin C per tablet by the number of tablets to find the total milligrams: \[ 500 \text{ mg/tablet} \times 240 \text{ tablets} = 120,000 \text{ mg}. \]

Step 3: Convert Total Milligrams to Grams

Convert the total milligrams of vitamin C to grams by dividing by 1000: \[ 120,000 \text{ mg} \div 1000 = 120 \text{ g}. \]

Step 4: Confirm the Units

Ensure that the final result is in grams, as required by the problem statement.

Key Concepts

Understanding Milligrams to Grams Conversion

When dealing with measurements, especially in the metric system, understanding units is crucial for accuracy. Milligrams and grams are both units of mass in this system, with milligrams being a smaller unit because there are 1,000 milligrams in a single gram. This means that to convert milligrams to grams, you simply divide the number of milligrams by 1,000. For example, if you have 1,000 milligrams, dividing by 1,000 gives you 1 gram.
This conversion is key when you need to switch between units. It can help in various contexts like science, cooking, or medicine, where precise measurement is important. Making these conversions correctly ensures that you work with the right amount of a substance, as in our vitamin C example.

Easy Ways to Multiply Quantities

Multiplying quantities is a straightforward yet critical mathematical operation that you often use when you want to find the total amount of something. In this example, you're calculating the total amount of vitamin C in the tablets. Each tablet contains a specific amount of vitamin C (500 mg), and the bottle has a total of 240 tablets.
To find the total milligrams of vitamin C, multiply the 500 milligrams per tablet by the 240 tablets. This calculation is simple: a multiplication of a singular value by the number of items gives you the total amount in milligrams:

• Calculate: (500 mg/tablet) * 240 tablets = 120,000 mg.

Breaking it down step-by-step ensures you don't mix up the quantities and helps in keeping track of the units, avoiding errors that could lead to incorrect results.

Step-by-Step Problem-Solving Process

Solving problems, particularly those involving multiple steps, can be intimidating, but following a structured approach can make it manageable. Here, the problem-solving process involves a few critical steps, each building upon the last. The first step is to clearly understand what is being asked and the relationship between the quantities involved. In our example, recognizing the conversion from milligrams to grams is the crucial aspect.
Once you have an understanding of the unit conversion, you move to multiplying the given values. After calculating the total, you apply your knowledge of unit conversion to shift the result from milligrams to grams. This structured approach helps you tackle complex problems with confidence:

• Identify what the problem is asking for.
• Break the problem into smaller parts.
• Perform calculations step by step, ensuring you keep track of units.
• Convert and adjust units as necessary to meet the requirements of the question.

Following such a methodical approach not only prevents mistakes but also builds a robust understanding of the concepts involved, enabling you to apply them correctly to varied scenarios.