Peter is considering purchasing an item that costs $\$ 19$. The sales tax in Peter's area is set at $5.8 \%$. How much sales tax would be charged on this purchase? Round your answer to the nearest cent, if necessary.

Step 1 ：Let's denote the cost of the item as \(C\), which is given as \$19.

Step 2 ：The sales tax rate is given as \(5.8\% \), which we can express as a decimal by dividing by 100, giving us \(0.058\).

Step 3 ：We can calculate the sales tax charged on the purchase by multiplying the cost of the item by the sales tax rate, \(C \times 0.058\).

Step 4 ：Substituting the given values, we get \(19 \times 0.058\), which equals \$1.1.

Step 5 ：Final Answer: The sales tax charged on the purchase would be \(\boxed{1.1}\) dollars.