during a cross-country road trip, nathan predicts that he will average 22.6 miles per gallon. during the trip, he drives 2,882 miles and uses 131 gallons of gas. calculate his percent error, rounded to the nearest whole percent
Actual MPG = 2,882 / 131 = 22.1
Percent Error = (22.6 - 22.1) / 22.1 x 100 = 2.3%
Rounded to the nearest whole percent = 2%
To calculate the percent error, we need to compare Nathan's predicted average with the actual average.
The predicted average is given as 22.6 miles per gallon. The actual average can be calculated by dividing the total distance driven by the total amount of gas used.
Actual average = Total distance driven / Total amount of gas used
= 2,882 miles / 131 gallons
≈ 22.027 miles per gallon
Now we can calculate the percent error using the formula:
Percent error = ((|Predicted Value - Actual Value|) / Actual Value) * 100
Percent error = ((|22.6 - 22.027|) / 22.027) * 100
= (0.573 / 22.027) * 100
≈ 2.6
Therefore, Nathan's percent error, rounded to the nearest whole percent, is approximately 3%.
To calculate the percent error, we can use the following formula:
Percent Error = (|Measured Value - Predicted Value| / Predicted Value) * 100
In this case, the measured value is the actual average miles per gallon Nathan achieved, and the predicted value is his initial prediction of 22.6 miles per gallon.
Measured Value = Total Miles Driven / Total Gallons Used
Measured Value = 2,882 miles / 131 gallons
Measured Value ≈ 22.02 miles per gallon
Now, let's plug in the values into the percent error formula:
Percent Error = (|Measured Value - Predicted Value| / Predicted Value) * 100
Percent Error = (|22.02 - 22.6| / 22.6) * 100
Percent Error ≈ (0.58 / 22.6) * 100
Percent Error ≈ 0.0256 * 100
Percent Error ≈ 2.56
Therefore, the percent error, rounded to the nearest whole percent, is approximately 3%.