Write and solve a proportion to complete the statement. Round your answer to the nearest hundredth. 2.5 L ? gal
The Correct Answer and Explanation is :
To convert 2.5 liters to gallons, we can set up a proportion using the conversion factor between liters and gallons. The conversion factor is:
[
1 \text{ gallon} = 3.785 \text{ liters}
]
Step 1: Set up the proportion
We want to find how many gallons are equivalent to 2.5 liters. Let’s call this unknown value ( x ) gallons. The proportion is:
[
\frac{1 \text{ gallon}}{3.785 \text{ liters}} = \frac{x \text{ gallons}}{2.5 \text{ liters}}
]
Step 2: Solve the proportion
Now, cross-multiply and solve for ( x ):
[
1 \times 2.5 = 3.785 \times x
]
[
2.5 = 3.785x
]
Next, divide both sides by 3.785 to solve for ( x ):
[
x = \frac{2.5}{3.785}
]
[
x \approx 0.6604
]
So, 2.5 liters is approximately ( 0.66 ) gallons when rounded to the nearest hundredth.
Explanation
In this problem, we used the known conversion factor between liters and gallons. To solve, we set up a proportion, which compares two ratios—one with the known values and one with the unknown we are solving for. By cross-multiplying and solving for the unknown, we found that 2.5 liters is about 0.66 gallons.
Proportions are a useful method when converting units because they maintain the relationship between two quantities. When dealing with measurements that can be expressed in different units (such as liters and gallons), proportions help us ensure that the conversion is accurate, especially when rounding to the nearest hundredth.
This technique is not only applicable in volume conversions but also in many other areas of math and science, such as calculating rates, scaling recipes, or understanding map distances.