Question

Several years ago, pharmacists used the Apothecary System of Measurement. In this system, 1 scruple is equal to 20 grains (gr). There are \(480 \mathrm{gr}\) in \(1 \mathrm{oz}\), and in this system, there are \(373 \mathrm{~g}\) in \(12 \mathrm{oz}\). How many scruples would be in \(695 \mathrm{~g}\) ?

Short answer

Approximately 536.64 scruples.

Step-by-step solution

Understand the Given Information

First, identify all the conversions provided: 1. 1 scruple = 20 grains (gr)2. 480 gr = 1 oz3. 373 grams (g) = 12 oz

Convert Grams to Ounces

Use the conversion rate between grams and ounces to find out how many ounces are in 695 grams. Given: 373 g = 12 ozTo find the number of ounces in 695 grams, set up a proportion:\ \[ \frac{373 \, \text{g}}{12 \, \text{oz}} = \frac{695 \, \text{g}}{x \, \text{oz}} \]Solve for \(x\):\( x = \frac{695 \, \text{g} \times 12 \, \text{oz}}{373 \, \text{g}} \)\( x \approx 22.36 \, \text{oz} \)

Convert Ounces to Grains

Convert the number of ounces to grains using the given conversion rate. Given: 1 oz = 480 gr\[\text{Total grains} = 22.36 \, \text{oz} \times 480 \, \text{gr/oz} \]\(\text{Total grains} \approx 10732.8 \, \text{gr} \)

Convert Grains to Scruples

Finally, convert the total grains to scruples. Given: 1 scruple = 20 gr\(\text{Total scruples} = \frac{10732.8 \, \text{gr}}{20 \, \text{gr/scruple}} \)\(\text{Total scruples} \approx 536.64 \, \text{scruples} \)

Key concepts

unit conversion

Unit conversion is an important skill, especially in fields like pharmacology where different systems of measurement may be used.
In this exercise, we convert between grams, ounces, grains, and scruples.
To solve the problem, we need to move from one unit to another in a structured way.
Here's how we do that:

• Convert grams to ounces using the given ratio.
• Convert ounces to grains.
• Convert grains to scruples.

By understanding these conversion factors and using proportions, we can easily navigate between different units. Using proportions simplifies complex conversions by breaking them into smaller, more manageable steps.
For example, to find how many ounces are in 695 grams, we use the known ratio of 373 grams to 12 ounces. Then we solve for the unknown by cross-multiplying and dividing.
In general, whenever faced with unit conversion problems, identify all given conversion factors, set up proportions correctly, and solve step-by-step.
Each step builds on the previous one, ensuring accuracy and clarity throughout the conversion process.

pharmacy calculations

Pharmacy calculations are essential for ensuring accurate dosages and preparing medications safely. This exercise highlights an example of such calculations.
Pharmacists must be adept at converting various units of measurement to prepare the right amount of medication.

• First, we converted grams to ounces.
• Then, ounces to grains.
• Finally, grains to scruples.

Each of these steps is crucial for accurate measurements. Understanding these conversions ensures that pharmacists dispense safe and effective doses.
Accuracy in calculations prevents under-dosing or overdosing, both of which can have serious consequences.
Pharmacists often rely on conversion charts and formulas but must be vigilant to double-check their work for safety.
Mastering these calculations helps in maintaining the integrity and trust in the pharmacy profession.
It is vital to practice these conversions regularly to develop a strong proficiency, ensuring that every prescription is filled accurately and safely.

historical measurement systems

The Apothecary System of Measurement is a historical system once used by pharmacists.
This system included units like scruples, grains, and ounces.

• 1 scruple = 20 grains (gr).
• 480 gr = 1 oz.

These units are different from the metric system or even the more commonly used imperial system today.
Understanding historical measurement systems helps in interpreting older medical texts and prescriptions.
Even though the Apothecary System is largely obsolete, knowledge of it can be valuable for academic and historical purposes.
This exercise demonstrates how these old units can still be converted and understood using modern methods.
Despite its decline, the study of such systems provides insight into the history of pharmacy and medicine.
Learning about historical systems like the Apothecary System enriches our understanding of the evolution of medical practices and measurement standards.