Estimate an answer by rounding each number to one nonzero digit first, then perform the actual calculation. Ajet fuel tank containing \( 12,857.8 \) gallons is being emptied at a rate of 121.3 gallons per minute. How many minutes will it take to empty the tank? Estimated value: \( \square \) minutes Actual value: \( \square \) minutes

To estimate the time it will take to empty the jet fuel tank, we first round each number to one nonzero digit. 1. **Round \( 12,857.8 \) gallons:** - The first nonzero digit is \( 1 \) (in the thousands place). - Rounding \( 12,857.8 \) to one nonzero digit gives us \( 10,000 \) gallons. 2. **Round \( 121.3 \) gallons per minute:** - The first nonzero digit is \( 1 \) (in the hundreds place). - Rounding \( 121.3 \) to one nonzero digit gives us \( 100 \) gallons per minute. Now, we can estimate the time to empty the tank using these rounded values: \[ \text{Estimated time} = \frac{\text{Estimated gallons}}{\text{Estimated rate}} = \frac{10,000 \text{ gallons}}{100 \text{ gallons/minute}} = 100 \text{ minutes} \] Now, let's calculate the actual time using the original values: \[ \text{Actual time} = \frac{12,857.8 \text{ gallons}}{121.3 \text{ gallons/minute}} \] Calculating this gives: \[ \text{Actual time} \approx 106.1 \text{ minutes} \] So, the final answers are: Estimated value: \( 100 \) minutes Actual value: \( 106.1 \) minutes