Step 1 :Let the cost of the item be denoted as \(cost\_of\_item = 15\)
Step 2 :The sales tax rate is given as \(sales\_tax\_rate = 7.5 / 100 = 0.075\)
Step 3 :The sales tax charged on the purchase can be calculated as \(sales\_tax = cost\_of\_item * sales\_tax\_rate = 1.125\)
Step 4 :Rounding the sales tax to the nearest cent gives \(rounded\_sales\_tax = round(sales\_tax, 2) = 1.12\)
Step 5 :Final Answer: The sales tax charged on the purchase would be \(\boxed{1.12}\) dollars.