How many liters of gasoline are needed to fill a 13.2-gallon tank? There are about 1.06 quarts per liter. Round to the nearest tenth for the variable indicated.
The Correct Answer and Explanation is:
To find how many liters of gasoline are needed to fill a 13.2-gallon tank, we first need to understand the relationship between gallons, quarts, and liters.
Step 1: Convert Gallons to Quarts
Since 1 gallon = 4 quarts,
we multiply the number of gallons by 4:
13.2 gallons × 4 = 52.8 quarts
Step 2: Convert Quarts to Liters
We are told that there are about 1.06 quarts per liter, so we divide the number of quarts by 1.06 to convert to liters:
52.8 quarts ÷ 1.06 ≈ 49.8 liters
Final Answer: 49.8 liters
Explanation (Approx. 300 Words)
To convert a volume from gallons to liters, we can use a multi-step conversion process based on known relationships between different units. In this problem, we start with 13.2 gallons of gasoline and aim to express this quantity in liters. This type of unit conversion is common in science, automotive contexts, and international travel where metric units are often preferred.
First, we convert gallons to quarts, because the conversion from quarts to liters is directly provided. There are exactly 4 quarts in 1 gallon. Therefore, multiplying the 13.2 gallons by 4 gives 52.8 quarts. This means that a 13.2-gallon tank holds 52.8 quarts of gasoline.
Next, we convert from quarts to liters. The given conversion factor is approximately 1.06 quarts per liter. Since we have the number of quarts and want to find the number of liters, we divide the number of quarts by 1.06. That is:
52.8 ÷ 1.06 ≈ 49.8 liters.
Thus, to fill a 13.2-gallon tank, you would need approximately 49.8 liters of gasoline. This value is rounded to the nearest tenth as instructed. It’s important to understand that small rounding errors may exist in practical applications, especially due to the approximate nature of the conversion factor (1.06 quarts per liter is a rounded value itself).
Using dimensional analysis and unit conversions like this is a powerful technique in science and everyday life, helping us compare and communicate measurements across different systems.
