Questions: A nickel is found to have a volume of 2.81 * 10^4 liters. Show, using unit analysis, what the volume of the nickel is in quarts.

A nickel is found to have a volume of 2.81 * 10^4 liters. Show, using unit analysis, what the volume of the nickel is in quarts.
Transcript text: A nickel is found to have a volume of 2.81 * 10^4 liters. Show, using unit analysis, what the volume of the nickel is in quarts.
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Solution

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Solution Steps

Step 1: Identify the Given Volume

The given volume of the nickel is 2.81×1042.81 \times 10^4 liters.

Step 2: Identify the Conversion Factor

We need to convert liters to quarts. The conversion factor between liters and gallons is given as: 3.79L=1gal 3.79 \, \text{L} = 1 \, \text{gal}

We also know that: 1gal=4qt 1 \, \text{gal} = 4 \, \text{qt}

Step 3: Convert Liters to Gallons

First, convert the volume from liters to gallons: 2.81×104L×1gal3.79L 2.81 \times 10^4 \, \text{L} \times \frac{1 \, \text{gal}}{3.79 \, \text{L}}

Step 4: Convert Gallons to Quarts

Next, convert the volume from gallons to quarts: (2.81×104L×1gal3.79L)×4qt1gal \left( 2.81 \times 10^4 \, \text{L} \times \frac{1 \, \text{gal}}{3.79 \, \text{L}} \right) \times \frac{4 \, \text{qt}}{1 \, \text{gal}}

Step 5: Perform the Calculation

Combine the conversion factors and perform the calculation: 2.81×104×43.79 2.81 \times 10^4 \times \frac{4}{3.79}

=2.81×104×1.0554 = 2.81 \times 10^4 \times 1.0554

=2.9667×104qt = 2.9667 \times 10^4 \, \text{qt}

Final Answer

2.9667×104qt\boxed{2.9667 \times 10^4 \, \text{qt}}

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