If an automobile’s gas mileage is 22 km/L, what is this quantity in miles per gallon? 1 m = 0.000621371 mi 1 L = 0.264172 gal 1 km = 1000 m – Report the answer using the correct number of significant figures – Do not include units
The Correct Answer and Explanation is:
To convert the automobile’s gas mileage from kilometers per liter (km/L) to miles per gallon (mi/gal), we will use the provided conversion factors step by step.
Given Data:
- Gas mileage: 22 km/L
- Conversion factors:
- 1 meter (m) = 0.000621371 miles (mi)
- 1 liter (L) = 0.264172 gallons (gal)
- 1 kilometer (km) = 1000 meters (m)
Conversion Process:
- Convert kilometers to miles:
- Since 1 km = 1000 m, the total distance in meters is: 22 km=22×1000=22000 m22 \, \text{km} = 22 \times 1000 = 22000 \, \text{m}22km=22×1000=22000m
- Now convert meters to miles using the conversion factor 1 m=0.000621371 mi1 \, \text{m} = 0.000621371 \, \text{mi}1m=0.000621371mi: 22000 m×0.000621371 mim=13.667 mi22000 \, \text{m} \times 0.000621371 \, \frac{\text{mi}}{\text{m}} = 13.667 \, \text{mi}22000m×0.000621371mmi=13.667mi
- Therefore, 22 km is equivalent to 13.667 miles.
- Convert liters to gallons:
- We know that 1 L = 0.264172 gallons, so: 1 L=0.264172 gal1 \, \text{L} = 0.264172 \, \text{gal}1L=0.264172gal
- Therefore, the gas mileage in miles per gallon is: 13.667 mi/L÷0.264172 gal/L=51.8 mi/gal13.667 \, \text{mi/L} \div 0.264172 \, \text{gal/L} = 51.8 \, \text{mi/gal}13.667mi/L÷0.264172gal/L=51.8mi/gal
Final Answer:
After rounding to the correct number of significant figures (two significant figures based on the input data), the gas mileage is approximately: 51.8\boxed{51.8}51.8
Explanation:
- The conversion process involved converting kilometers to meters, then meters to miles. After that, we converted liters to gallons. The resulting mileage was then calculated by dividing the distance in miles by the volume in gallons.
- The correct number of significant figures is two, as the given data (22 km/L) has two significant figures, so the final result is reported as 51.8 mi/gal
