To determine the correct conversion ratios between gallons and liters, let's analyze the given options with detailed reasoning:
1. Option: [tex]\( 0.264 \, \text{gal} \, / \, 1 \, \text{L} \)[/tex]
- This ratio states that 1 liter is equivalent to 0.264 gallons. This is a valid conversion ratio as 1 liter is indeed approximately equal to 0.264 gallons.
2. Option: [tex]\( 3.79 \, \text{L} \, / \, 1 \, \text{gal} \)[/tex]
- This ratio states that 1 gallon is equivalent to 3.79 liters. This is another valid conversion ratio as 1 gallon is indeed approximately equal to 3.79 liters.
3. Option: [tex]\( 1 \, \text{gal} \, / \, 3.79 \, \text{L} \)[/tex]
- This ratio suggests that 1 gallon is equivalent to 3.79 liters, but it implies a reciprocal relationship (suggesting that 3.79 liters is equivalent to 1 gallon), which is incorrect. So, this is not a valid conversion ratio.
4. Option: [tex]\( 1 \, \text{L} \, / \, 0.264 \, \text{gal} \)[/tex]
- This ratio suggests that 1 liter is equivalent to 0.264 gallons, but like the third option, it implies a reciprocal relationship (suggesting that 0.264 gallons is equivalent to 1 liter), which is incorrect. Consequently, this is not a valid conversion ratio.
In summary, the correct conversion ratios are:
- [tex]\( 0.264 \, \text{gal} \, / \, 1 \, \text{L} \)[/tex]
- [tex]\( 3.79 \, \text{L} \, / \, 1 \, \text{gal} \)[/tex]
These two ratios accurately represent the respective conversions between gallons and liters.
