anonymous
  • anonymous
A particular brand of gasoline has a density of 0.737 g/mL at 25 ∘C. How many grams of this gasoline would fill a 13.7gal tank?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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mathstudent55
  • mathstudent55
This is a problem of unit conversions. Do you know how to convert gallons into liters?
anonymous
  • anonymous
unfortunately no :( im not very good at converting
mathstudent55
  • mathstudent55
1 gal = 3.785 liter (approximately) 1 liter = 1000 ml

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mathstudent55
  • mathstudent55
Each conversion factor can be written as a fraction. By multiplying the number of gallons by how many liters in a gallon, you get liters. \( 13.7 ~gal \times \dfrac{3.785 ~liter}{1~gal} \)
mathstudent55
  • mathstudent55
Now you multiply that by how many milliliters in a liter to get milliliters.
anonymous
  • anonymous
so 51854.5 ml?
mathstudent55
  • mathstudent55
\( 13.7 ~gal \times \dfrac{3.785 ~liter}{1~gal} \times \dfrac{1000~ml}{1~liter} \) Since you want the answer to be in grams, now you multiply by a fraction that involves the density in a way that will have grams in the numerator and ml in the denominator: \( 13.7 ~gal \times \dfrac{3.785 ~liter}{1~gal} \times \dfrac{1000~ml}{1~liter} \times \dfrac{0.737 ~g}{ml} = ~?\)
mathstudent55
  • mathstudent55
Yes, your number above is correct. That was the number of ml. Now multiply by the last fraction in the conversion.
anonymous
  • anonymous
Thank you soooo much! I have been stuck on that problem for the last hour. I really appreciate all your help.
mathstudent55
  • mathstudent55
Notice what happens to the units: \( 13.7 ~\cancel{\color{green}{gal}} \times \dfrac{3.785 ~\cancel{\color{red}{liter}}}{1~\cancel{\color{green}{gal}}} \times \dfrac{1000~\cancel{\color{blue}{ml}}}{1~\cancel{\color{red}{liter}}} \times \dfrac{0.737 ~g}{\cancel{\color{blue}{ml}}} = ~?\) After all other units cancel out, only grams remains.
mathstudent55
  • mathstudent55
You're welcome.

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