chemistry
posted by taysha on .
an automobile gives gas mileage of 32 miles/gal, what would be the mileage in km/L? [1 gal=3.78L 1km=0.621miles]

In conversion problems like this you should note three things.
1. All of them start with the number to be converted, in this case 32 mi/gal.
2. All are multiplied by a factor. In this case there are TWO factors but the idea is the same. You have the factors listed; i.e., 1 gal = 3.78 L and 1 km = 0.621 miles.
3. The factor is arranged so that the units we don't want to keep cancel out leaving the units we want to keep.
Just go down step 1, step 2, step 3. Therefore, in this problem, we have
32 mi/gal x factor = ?? km/L (steps 1 and 2)
Now step 3. Arrange the factors, similar to the problem converting mg/dL to g/L so that the units we don't want (miles/gal) cancel to leave the units we want to keep (km/L).
Post your work if you get stuck and explain what yoy don't understand. 
ok so i did 32miles = 1 km/0.621 miles. miles cancel leaving 19.872 km
where does the L part come in is my answer right? 
ok so i did 32miles = 1 km/0.621 miles. miles cancel leaving 19.872 km
where does the L part come in is my answer right? 
No, it isn't correct BECAUSE (and you have already noted this) the units DON'T end up with km/L. AND you used only one factor. I will do one factor.
What are the factors again? You have them in the first post. 1 gal = 3.78 L and 1 km = 0.621 mi. Let't take these factors one at a time.
First, the 1 gal = 3.78 L. There are ONLY TWO ways you may use this factor. One is 1 gal/3.78 L AND the other is 3.78 L/1 gal.
The second factor is 1 km = 0.621 mi. Likewise, there are ONLY two ways to use this factor. One is 1 km/0.621 mi and the other is 0.621 mi/1 km.
So we have only step 3 to do. And that is the easy part because if we do it wrong the units we don't want don't cancel.
32 mi/gal x factor x factor = ??
Doing the first factor, let's try the two ways.
32 mi/gal x (0.621 mi/1 km) = some number but the units are mi^{2}/gal*km. We wanted to GET RID of the miles and this didn't do it. Let's try the other way.
32 mi/gal x (1 km/0.621 mi) = some number but the units are km/gal. Great. We got rid of the miles. True this isn't the answer BUT we converted the miles to km. Now you try converting the gal to L. Do it the same way to check that the gal cancels to leave km/L.
32 x (1 km/0.621 mi) x (factor) = km/L. 
261 nanometers to millimeters