Problem 43 - Prealgebra

Question

A patient is prescribed a dosage of Ceclor" of \(561 \mathrm{mg} .\) How many grams is the dosage?

Step-by-Step Solution

Answer

The dosage is 0.561 grams.

Step 1: Understand the Conversion Factor

To convert milligrams (mg) to grams (g), use the conversion factor: \(1 \, \text{gram} = 1000 \, \text{milligrams}\). This means that 1000 milligrams is equal to 1 gram.

Step 2: Set Up the Conversion Formula

To convert from milligrams to grams, use the formula: \[ \text{grams} = \frac{\text{milligrams}}{1000} \] For this exercise, substitute 561 milligrams into the formula.

Step 3: Perform the Calculation

Plug the given dosage into the formula: \[ \text{grams} = \frac{561}{1000} \]Perform the division to complete the conversion.

Step 4: Simplify the Result

Divide 561 by 1000 to find the answer: \[ \text{grams} = 0.561 \]Therefore, the dosage in grams is 0.561 g.

Key Concepts

Milligrams to Grams Conversion

Converting milligrams to grams is a fundamental skill in math and science, often encountered in medication dosages, cooking measurements, and scientific experiments. At the core is the understanding that 1 gram is equal to 1000 milligrams.

This means if you have a substance amount given in milligrams and need to know how many grams it equates to, you divide the milligram value by 1000. For example, if a prescription is for 561 milligrams, the conversion would be:

• Take the milligram value.
• Divide by 1000.
• Result is in grams.

By following these simple steps, you can confidently convert milligrams to grams in any situation.

Dimensional Analysis

Dimensional analysis is a powerful tool that helps in unit conversion by using conversion factors.

Here's how dimensional analysis works in converting milligrams to grams:

• You start with the quantity you want to convert (e.g., 561 mg).
• Apply the conversion factor, knowing that 1 gram = 1000 milligrams.
• Use the formula: \[ \text{grams} = \frac{\text{milligrams}}{1000} \]

By setting up this equation, you're essentially cancelling out the milligrams unit and introducing the grams unit.

This method isn't just for grams; it's a versatile approach applicable to any unit conversion challenge. It ensures precision and understanding, helping avoid errors in calculations.

Math Problem-Solving

Math problem-solving is essential, especially when it involves practical applications like medication dosages.

Here's how you can effectively tackle unit conversion problems:

• Break down the problem - Identify what is being asked.
• Choose the right formula or conversion factor.
• Carefully substitute the values into the formula.
• Carry out the calculations step by step.
• Simplify the final result.

With the given problem, after identifying that the conversion from milligrams to grams is required, apply the appropriate formula, as demonstrated in the example: \[\text{grams} = \frac{561}{1000} = 0.561 \,\text{grams}\]

Practicing these steps can enhance accuracy and build confidence in tackling various math problems.