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Chapter 4: Problem 58

Find the gas mileage rounded to the nearest tenth. \(396 \mathrm{mi} ; 17 \mathrm{gal}\)

Short Answer

Expert verified
The gas mileage is 23.3 mpg.

Step by step solution

01

- Identify Given Values

Determine the values provided in the exercise: the distance traveled is 396 miles and the amount of gas used is 17 gallons.
02

- Calculate Gas Mileage

To find the gas mileage, divide the total distance traveled by the amount of gas used. Use the formula: \[ \text{Gas Mileage} = \frac{\text{Distance}}{\text{Gas Used}} = \frac{396 \text{ miles}}{17 \text{ gallons}} \]
03

- Perform the Division

Divide 396 by 17 to get the gas mileage in miles per gallon (mpg). \[ \frac{396}{17} \ \text{Gas Mileage} \ \text{Gas Mileage} \ = 23.2941 \]
04

- Round to the Nearest Tenth

Round the result obtained in Step 3 to the nearest tenth. The first decimal place is 2, and the number after it is 9, which means we round up. Therefore, 23.2941 rounded to the nearest tenth is 23.3.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distance and Fuel Consumption
Understanding distance and fuel consumption is crucial when calculating gas mileage. Distance refers to how far a vehicle has traveled. In our exercise, the distance is 396 miles. Fuel consumption tells us how much gas the vehicle used for that distance. Here, 17 gallons of gas were consumed.
This basic information helps set up our calculations. Anytime you have a distance and the gas consumption, you can proceed to find out how efficiently the vehicle used the fuel.
Miles Per Gallon (mpg)
Miles per gallon (mpg) is a measure of a vehicle's fuel efficiency. To calculate it, we use the distance traveled and the amount of fuel used. The formula for mpg is:
\[ \text{Gas Mileage} = \frac{\text{Distance}}{\text{Gas Used}} \]
In the given exercise, the distance is 396 miles, and the gas used is 17 gallons. Plugging these values into the formula, we get:
\[ \frac{396 \text{ miles}}{17 \text{ gallons}} = 23.2941 \text{ mpg} \]
This means the vehicle traveled approximately 23.2941 miles for every gallon of gas consumed.
Rounding Numbers
Rounding numbers is an essential skill in math, ensuring we simplify our results for practical use. In our exercise, we need to round the gas mileage to the nearest tenth. Here鈥檚 how you would do it:
Firstly, look at the number in the first decimal place. In our case, it's 2 (from 23.2941). Next, check the number right after this decimal place. Here, it's 9.
If this number (9) is 5 or higher, you round the first decimal place up by one. Since 9 is greater than 5, we round 23.2941 up to 23.3. Hence, 23.2941 rounded to the nearest tenth is 23.3.
This rounding makes it easier to communicate and understand the gas mileage without losing significant accuracy.

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