Answer
a. Yes, they are the same
b. 1.00 oz troy
c. 7.72 grains ap or 0.386 scruples
d. 1.296 grams
Work Step by Step
a.
$\text{1 grain ap} \times \frac{\text{1 scruple}}{\text{20 grain ap}}\times \frac{\text{1 dram ap}}{\text{3 scruples}}\times \frac{\text{3.888g}}{\text{1 dram ap}}$ = 0.06480 g
We also know from question 45 that 1 grain troy = 0.06480 g
Thus, the two are the same.
b.
$\text{1 oz ap} \times \frac{\text{8 dram ap}}{\text{1 oz ap}}\times \frac{\text{3.888 g}}{\text{1 dram ap}}\times \frac{\text{1 oz troy}}{\text{31.1 g}}$ = 1.00 oz troy
c.
$5.00 \times 10^{2}\text{ mg} \times \frac{\text{1 g}}{\text{1000 mg}}\times \frac{\text{1 dram ap}}{\text{3.888 g}}\times \frac{\text{3 scruples}}{\text{1 dram ap}}$ = 0.386 scruples
$0.386\text{ scruples} \times \frac{\text{20 grains ap}}{\text{1 scruple}}$ = 7.72 grains ap
d.
$\text{1 scruple} \times \frac{\text{1 dram ap}}{\text{3 scruples}}\times \frac{\text{3.888 g}}{\text{1 dram ap}}$ = 1.296 g
