Problem 36 - Prealgebra

Question

A bottle of maximum- strength aspirin contains 90 tablets. Each tablet contains \(500 \mathrm{mg}\) of aspirin. How many total grams of aspirin are in this bottle?

Step-by-Step Solution

Answer

The bottle contains 45 grams of aspirin.

Step 1: Understand the Problem

We need to determine the total amount of aspirin in a bottle containing 90 tablets, where each tablet has 500 mg of aspirin.

Step 2: Convert Milligrams to Grams

Since each tablet contains 500 milligrams and 1000 milligrams is equal to 1 gram, we need to convert the 500 mg in each tablet to grams using the conversion formula: \[ \text{Grams} = \frac{\text{Milligrams}}{1000} \].

Step 3: Calculate Aspirin per Tablet in Grams

Convert the aspirin in one tablet from milligrams to grams: \[ \text{Grams per Tablet} = \frac{500 \text{ mg}}{1000} = 0.5 \text{ grams} \].

Step 4: Calculate Total Aspirin in the Bottle

Multiply the grams per tablet by the total number of tablets: \[ \text{Total Aspirin in Grams} = 90 \times 0.5 = 45 \text{ grams} \].

Key Concepts

Milligrams to Grams

When we talk about converting milligrams (mg) to grams (g), it's like moving between two units of the same type, like feet to inches. Both measure weight, but they do so at different scales.
A milligram is a thousandth of a gram, which means there are 1000 milligrams in just one gram. This is a key conversion factor in many scientific and everyday calculations.
The formula for conversion is simple but crucial: \[ \text{Grams} = \frac{\text{Milligrams}}{1000} \]This formula helps us understand that "mg" means smaller portions of "g." For instance, if you have something weighing 500 mg, you simply divide by 1000 to find out it's 0.5 g. This conversion is especially helpful in pharmacy and medicine, where precise dosages are critical.

Tablet Dosage Calculation

Calculating the dosage of a tablet is a critical task in healthcare to ensure proper treatment.
To find the total dosage in a bottle of pills, you first determine how much of the active ingredient is in one tablet. Combine this with the total number of tablets to get a comprehensive measure.
Here's the approach broken down into steps:

• First, know the dose per tablet, which is 500 mg in this case.
• Next, convert the dose per tablet into grams using our above conversion: 500 mg becomes 0.5 g.
• Multiply the converted dose per tablet by the total number of tablets (90 tablets in this case).

This gives a total aspirin amount of:\[ \text{Total Grams} = 90 \times 0.5 = 45 \text{ grams} \]Understanding this process means recognizing the importance of each step to ensure dosage accuracy and patient safety.

Problem Solving Steps

Problem-solving is key in many aspects of science, from physics to pharmacy. Breaking down a problem into manageable steps makes it easier to tackle.
Let's see our problem-solving steps through the lens of the given aspirin problem:

• **Step 1:** Understand the problem - Identify what you're asked to find. For us, it's the total grams of aspirin in the bottle.
• **Step 2:** Convert units where necessary - Milligrams to grams is crucial for accurate calculations.
• **Step 3:** Calculate per unit measurement - Know how much aspirin is in each tablet in grams.
• **Step 4:** Calculate the total - From individual units, calculate totals (total for one bottle in this instance).

Each step builds on the previous one, ensuring nothing is missed and clarity is maintained. This structured approach helps avoid mistakes and streamlines the process in mathematical and real-life scenarios alike.