Donny Dont was asked what mass in kg a substance must have if its density is 3.00 kg/L and it takes up 12.0 gallons of volume.

Question

Donny Dont was asked what mass in kg a substance must have if its density is 3.00 kg/L and it takes up 12.0 gallons of volume. He correctly rearranged the equation for density, d=m/V, to solve for m: m=V*d, but what he put for his answer was “12.0 gal. * 3.00 kg / Liter = 36”.  Ohhhhh noooo!! Donny Dont didn’t include any units after the number 36, and therefore his answer doesn’t really convey any information! He multiplied 12 * 3 correctly, but neglected to multiply or divide units. What units would his answer of 36 be in? Hint: it is a big jumbled mess of units. 

   Ohhh noooo! Donny also failed to answer with the correct number of significant figures! How many sig figs SHOULD his answer contain?

  To correctly do this problem, we need to get the units of volume to cancel, and to do that, we need to make them consistent, perhaps by converting 12.0 gal. to Liters, and then using that number of Liters for V (Conversion factor: There are 3.78 L per gallon). Finish the problem correctly for Donny, so that kg is the unit of your answer, and so that your answer has the correct number of significant figures! 

Answer 1

Poor Donny mixed up his units. Let's sort this out.

What units should the 36 be in?

12.0 gal. x 3.00 kg / Liter = 36

If we ignore the numbers, we can see the units are gallons x kg / liter.

So his answer is 36 gal kg / l

How many sig figs SHOULD his answer contain?

Donny messed up again and ignored sig figs. We can see our initial data is 12.0 gal and 3.00 kg. Each number has 3 sig figs, so the final answer should have 3 sig figs. Should be 36.0 gal kg / l

Finally lets fix the units problem.

We'll want to get rid of the 2 different volume units be remembering that there are 3.78 l / gal.

Using this conversion factor let's cancel out some units:

36.0 gal kg l^-1 x 3.78 l gal^-1

The liters and gallons cancel, leaving us with:

136 kg

Finally a simple number of kg.