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Use dimensional analysis (the "factor-label" method) to solve the following problem. Show all steps needed to convert from starting units to ending units. Indicate all relationships needed before setting up and solving the problem.

Use any of the following relationships if needed:
- 1 mile = 1760 yds
- 16 oz = 1 lb
- 1 L = 1.057 qts
- 1 day = 24 hours
- 1 yd = 3 ft
- 2000 lbs = 1 ton
- 4 qts = 1 gal
- 1 hour = 60 mins
- 1 ft = 12 in
- 1 oz = 28.35 g
- 32 oz = 1 qt
- 1 min = 60 secs
- 1 mile = 1.6093 km
- 1 kg = 2.205 lbs
- 1 qt = 2 pts

In the US, milk is sold by the gallon, while in Denmark it is sold by the liter. How many liters of milk would you need to equal one gallon?

Answer :

Final answer:

In Mathematics, particularly in unit conversions and measurements, you may be asked to convert between different units of measurement, in this case, gallons to liters. Using the factor-label method, we convert 1 gallon to quarts, then convert those quarts to liters, giving a result of 4.228 liters.

Explanation:

The question asks for a conversion from gallons to liters using dimensional analysis, also known as the factor-label method. This is a topic in Mathematics, specifically in the branch of unit conversions and measurements. We'll conduct an in-depth solution and provide an accurate response to your inquiry.

One unique relationship we'll utilize to solve this problem is the conversion fact that 1 Gallon equals to 4 quarts (4 qts = 1 gal), and 1 Quart is approximately 1.057 Liters (1L = 1.057 qts).

Here are the steps for converting 1 gallon of milk into liters:

  1. Begin with the quantity you're aiming to convert: 1 Gallon.
  2. Using the conversion fact that 1 Gallon equals to 4 Quarts, we can set up the first conversion factor so that the gallon units cancel each other out: 1 Gallon x (4 Quarts / 1 Gallon)
  3. Finally, use the conversion fact that 1 Quart is equivalent to 1.057 Liters to set up the second conversion factor to cancel out the quarts unit: 4 Quarts x (1.057 Liters / 1 Quart)

The result of these steps is that 1 Gallon is approximately equal to 4.228 Liters of milk.

Learn more about Dimensional Analysis here:

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