The purity of gold is often measured in carats, where 24 carat is considered pure gold.
To convert the percentage purity to carats, use the following relationship:
\[
\text{Purity in carats} = \left( \frac{\text{Purity percentage}}{100} \right) \times 24
\]
Given that the purity is 58.33%, we calculate the carat equivalent as:
\[
\left( \frac{58.33}{100} \right) \times 24 = 14 \, \text{carat}
\]
Thus, the gold ring's purity can be alternatively shown as 14 carat.
Thus, the correct answer is option (3).