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Answer :
To solve this problem, we'll convert a given volume in cubic feet to gallons using the information from the table. We'll apply dimensional analysis, which is a method of using conversion factors to move from one set of units to another.
1. Identify the Known Conversion Factor:
From the table, we know that:
- 1 cubic foot is approximately equal to 7.48 gallons.
2. Determine the Volume to Be Converted:
Let's say we're given a volume of 1 cubic foot, and we need to convert this to gallons.
3. Perform the Conversion:
We use the conversion factor to find the equivalent number of gallons.
[tex]\[
\text{Volume in gallons} = \text{Volume in cubic feet} \times \text{Conversion factor}
\][/tex]
Plug in the values:
[tex]\[
\text{Volume in gallons} = 1 \text{ cubic foot} \times 7.48 \text{ gallons/cubic foot}
\][/tex]
This multiplication results in 7.48 gallons.
4. Round the Result:
According to the problem, we are asked to round to the nearest hundredth if needed. In this case, the calculated value is already rounded to two decimal places: 7.48.
Therefore, the volume is approximately 7.48 gallons when rounded to the nearest hundredth.
1. Identify the Known Conversion Factor:
From the table, we know that:
- 1 cubic foot is approximately equal to 7.48 gallons.
2. Determine the Volume to Be Converted:
Let's say we're given a volume of 1 cubic foot, and we need to convert this to gallons.
3. Perform the Conversion:
We use the conversion factor to find the equivalent number of gallons.
[tex]\[
\text{Volume in gallons} = \text{Volume in cubic feet} \times \text{Conversion factor}
\][/tex]
Plug in the values:
[tex]\[
\text{Volume in gallons} = 1 \text{ cubic foot} \times 7.48 \text{ gallons/cubic foot}
\][/tex]
This multiplication results in 7.48 gallons.
4. Round the Result:
According to the problem, we are asked to round to the nearest hundredth if needed. In this case, the calculated value is already rounded to two decimal places: 7.48.
Therefore, the volume is approximately 7.48 gallons when rounded to the nearest hundredth.
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Rewritten by : Barada
To convert a given measurement into gallons using dimensional analysis, follow these steps:
Identify the Given Measurement:
Suppose the given measurement is in cubic feet, let's assume you want to convert 3 cubic feet into gallons.Use the Conversion Factor:
From the table, we know that 1 cubic foot is approximately 7.48 gallons. This will be our conversion factor.Set Up the Conversion Equation:
To convert from cubic feet to gallons, multiply the number of cubic feet by the conversion factor:
[tex]\text{Gallons} = \text{Cubic Feet} \times \left(\frac{7.48 \text{ gallons}}{1 \text{ cubic foot}}\right)[/tex]Perform the Calculation:
Using the example of 3 cubic feet:
[tex]\text{Gallons} = 3 \text{ cubic feet} \times \left(\frac{7.48 \text{ gallons}}{1 \text{ cubic foot}}\right) = 22.44 \text{ gallons}[/tex]Round to the Nearest Hundredth:
The result, 22.44 gallons, is already rounded to the nearest hundredth.
This step-by-step method shows how to convert any volume unit based on the given table into gallons accurately.
