Determine the following estimate without using a calculator. Then use a calculator to perform the computation necessary to obtain an exact answer. How reasonable is your estimate when compared to the actual answer? Estimate the total cost of six grocery items if their prices are \( \$ 1.28, \$ 9.58, \$ 6.53, \$ 3.18, \$ 4.98 \), and \( \$ 0.39 \), by rounding each price to the nearest dollar and then adding. The estimate of the total cost of the grocery items is \( \$ \square \). (Type a whole number.)

First, let's round each of the given prices to the nearest dollar: - \( \$ 1.28 \) rounds to \( \$ 1 \) - \( \$ 9.58 \) rounds to \( \$ 10 \) - \( \$ 6.53 \) rounds to \( \$ 7 \) - \( \$ 3.18 \) rounds to \( \$ 3 \) - \( \$ 4.98 \) rounds to \( \$ 5 \) - \( \$ 0.39 \) rounds to \( \$ 0 \) Now, adding these rounded values together gives us: \( 1 + 10 + 7 + 3 + 5 + 0 = 26 \) So the estimate of the total cost of the grocery items is \( \$ 26 \). Next, let's calculate the actual total cost: - \( 1.28 + 9.58 + 6.53 + 3.18 + 4.98 + 0.39 \) Adding these gives approximately \( 1.28 + 9.58 = 10.86 \), then \( 10.86 + 6.53 = 17.39 \), followed by \( 17.39 + 3.18 = 20.57 \), and then \( 20.57 + 4.98 = 25.55 \), and finally \( 25.55 + 0.39 = 25.94 \). So, the exact total cost is \( \$ 25.94 \). Comparing the estimate of \( \$ 26 \) with the actual total of \( \$ 25.94 \), we see that the estimate is quite reasonable, being only \( 6 cents \) higher than the exact total! This shows that rounding can provide a good ballpark figure for budgeting before checking exact amounts.