Apothecaries (druggists) use the following set of measures...

Apothecaries (druggists) use the following set of measures in the English system: $$ \begin{aligned} 20 \text { grains ap } &=1 \text { scruple (exact) } \\ 3 \text { scruples } &=1 \text { dram ap (exact) } \\ 8 \text { dram ap } &=1 \mathrm{oz} \text { ap (exact) } \\ 1 \text { dram ap } &=3.888 \mathrm{~g} \end{aligned} $$ a. Is an apothecary grain the same as a troy grain? (See Exercise 45.) b. $102 \mathrm{ap}=$_____oz troy. c. An aspirin tablet contains $5.00 \times 10^{2} \mathrm{mg}$ of active ingredient. What mass in grains ap of active ingredient does it contain? What mass in scruples? d. What is the mass of 1 scruple in grams?

Apothecaries (druggists) use the following set of measures in the English system:
$$
\begin{aligned}
20 \text { grains ap } &=1 \text { scruple (exact) } \\
3 \text { scruples } &=1 \text { dram ap (exact) } \\
8 \text { dram ap } &=1 \mathrm{oz} \text { ap (exact) } \\
1 \text { dram ap } &=3.888 \mathrm{~g}
\end{aligned}
$$
a. Is an apothecary grain the same as a troy grain? (See Exercise 45.)
b. $102 \mathrm{ap}=$_____oz troy.
c. An aspirin tablet contains $5.00 \times 10^{2} \mathrm{mg}$ of active ingredient. What mass in grains ap of active ingredient does it contain? What mass in scruples?
d. What is the mass of 1 scruple in grams?

Key Concepts

Dimensional Analysis

Dimensional analysis is a technique used to convert units by treating conversion factors as fractions that can be multiplied with the given measurement. This method ensures that units cancel appropriately, leaving the desired unit as the final result. It is particularly useful when chaining multiple conversion factors together to navigate between several different units.

Metric Conversion

Metric conversion involves translating measurements from the English apothecary system to the metric system, such as converting drams or scruples to grams. This concept is important for comparing and understanding measurements across different systems, as it requires the application of known conversion factors between the units.

English Apothecary Measurement System

This concept refers to a historical system of mass measurements used by apothecaries, which includes units such as grains, scruples, drams, and ounces. Understanding this system is crucial as it explains how different units relate to each other through exact conversion factors, enabling the accurate measurement and preparation of medication.

Conversion Factors and Unit Relationships

Conversion factors form the backbone of unit conversion by providing exact numerical relationships between different units within a measurement system. In problems involving the apothecary system, these factors allow one to translate quantities from one unit to another by systematic multiplication or division, ensuring that quantities remain consistent across different units.

Measurement System Differences

This concept highlights the importance of recognizing and distinguishing between similar-sounding units from different measurement systems, such as the apothecary grain and the troy grain. A clear understanding of these differences ensures accurate conversions and prevents errors when translating measurements from one system to another.

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