Taking into account the change of units, the gold's density is 193000 [tex]\frac{decigrams}{L}[/tex].
The rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other), the direct rule of three must be applied. To solve a direct rule of three, the following expresion must be followed, where the unknown value D must be calculated using the known values A, B and C:
A ⇒ B
C ⇒ D
So, [tex]D=\frac{C*B}{A}[/tex]
The direct rule of three is the rule applied in this case where there is a change of units. To perform this conversion of units, you must first know that 1 gram = 10 decigrams. So, if 10 decigrams is equal to 1 gram, how many decigrams equals 19.3 grams?
1 gram ⇒ 10 decigrams
19.3 grams ⇒ D
So:
[tex]D=\frac{19.3 grams*10 decigrams}{1 gram}[/tex]
Solving:
D= 193 decigrams
On the other side, 1 mL = 0.001 L. Then:
[tex]\frac{19.3 grams}{mL} =\frac{193 decigrams}{0.001 L} = 193000 \frac{decigrams}{L}[/tex]
In summary, the gold's density is 193000 [tex]\frac{decigrams}{L}[/tex].
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