Determine the following estimate without using a calculator. Then use a calculator to perform the computation necessary to obtaln 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 \$2.08, \( \$ 5.46 \), \( \$ 13.95 \), \( \$ 11.73 \), \( \$ 9.05 \), and \( \$ 10.52 \), by rounding each price to the nearest dollar and then adding. The estimate of the total cost of the grocery litems is \( \$ \) 53 (Type a whole number.) The actual total cost of the grocery tiems is \$ \( \square \) .

To estimate the total cost of the grocery items, we will round each price to the nearest dollar and then add them together. Here are the prices rounded to the nearest dollar: 1. \( \$2.08 \) rounds to \( \$2 \) 2. \( \$5.46 \) rounds to \( \$5 \) 3. \( \$13.95 \) rounds to \( \$14 \) 4. \( \$11.73 \) rounds to \( \$12 \) 5. \( \$9.05 \) rounds to \( \$9 \) 6. \( \$10.52 \) rounds to \( \$11 \) Now, we will add these rounded values together: \[ 2 + 5 + 14 + 12 + 9 + 11 \] Calculating this step by step: 1. \( 2 + 5 = 7 \) 2. \( 7 + 14 = 21 \) 3. \( 21 + 12 = 33 \) 4. \( 33 + 9 = 42 \) 5. \( 42 + 11 = 53 \) So, the estimated total cost of the grocery items is \( \$53 \). Next, let's calculate the actual total cost by adding the original prices: \[ 2.08 + 5.46 + 13.95 + 11.73 + 9.05 + 10.52 \] Now, I will perform this calculation to find the exact total cost. Calculate the value by following steps: - step0: Calculate: \(2.08+5.46+13.95+11.73+9.05+10.52\) - step1: Add the numbers: \(52.79\) The actual total cost of the grocery items is \( \$52.79 \). Now, let's compare the estimate and the actual total: - Estimated total cost: \( \$53 \) - Actual total cost: \( \$52.79 \) The estimate of \( \$53 \) is very close to the actual total of \( \$52.79 \), showing that rounding to the nearest dollar provided a reasonable approximation. The difference is only \( \$0.21 \), which indicates that the estimate is quite accurate.