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?

Question

mathstudent55 · Answer

This is a problem of unit conversions.
Do you know how to convert gallons into liters?

anonymous · Answer

unfortunately no :( im not very good at converting

mathstudent55 · Answer

1 gal = 3.785 liter (approximately)
1 liter = 1000 ml

mathstudent55 · Answer

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 · Answer

Now you multiply that by how many milliliters in a liter to get milliliters.

anonymous · Answer

so 51854.5 ml?

mathstudent55 · Answer

$ 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 · Answer

Yes, your number above is correct. That was the number of ml. Now multiply by the last fraction in the conversion.

anonymous · Answer

Thank you soooo much! I have been stuck on that problem for the last hour. I really appreciate all your help.

mathstudent55 · Answer

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 · Answer

You're welcome.