Units when calculating original gravity

Ok so let me preface this with I'm an extract brewer currently and also a chemist. I'm reading John Palmer's "How to Brew" and his use of units is driving me nuts. Here's his way to calculate OG:
"If you want to brew 5 gal of 1.040 gravity beer, this would call for: 5lbs of DME having 40 pts/lb/gal or 5.5 lbs of LME having 36 pts/lb/gal."
Then here's his math:
" 40 pts/gal x 5 gal = 200 pts total. So if we want to use LME instead then...
200 pts = 36 pts/lb x (?)lbs so (?)lbs = 200/36= 5.55 lbs."
What??!! First off if the DME has 40 pts/lb/gal, then why in his calculation does he switch to 40 pts/gal. What happened to the lbs part?! Second, if it's 40 pts/lb/gal, that's really the same as saying it's 40 gal pts lb^-1 (gallon points per pound) is it not?? So why does John say 40 pts/gal?
Here's how I would do it, but I'd like to see what you science minded brewers think:
We want 5 gal of beer with 40 pts. So that's 5 gal x 40 pts = 200 gal pts.
Now we want to use a LME that has 36 pts/lb/gal ( aka 36 gal pts lb^-1).
So we do 200 gal pts x [(1lb)/(36 gal pts)] = 5.5 lbs.
Notice how in my math I get the same answer , AND my units actually work out.
So what do you guys (or gals) think??

Your dimensional analysis is clear, I like it. I'm a lazy guy w/a chemistry/biochem background and I use the $17.95 program, BeerSmith. It does all the calculations so I can worry about recipe formulation. By the way Beer Smith thinks standard DME, Amber DME more specifically has a 1.044 potential therefore that same 5 gal would yield 1.044 (44 pts)... When you start to mix a ratio of grist each having its own potential contribution the math becomes even more cumbersome, doable, I understand, but still.

When Palmer said 40 pts/gal, he really meant 40 pts/lb/gal. I wonder how many of his readers would understand 40 gal pts lb^-1?
Just a FYI, but 40 pppg is very low for DME. 46 pppg is generally considered the correct yield for DME.
Edit except in Beersmith, which uses 44 pppg /Edit

-a.

If you're smart enough to see Palmer's lax error, you're smart enough to understand what he means
I agree that using more complicated units would scare off even more homebrewers.

Personally, what gets me is recipes using percentages by weight instead of extract. Weight works fine as long as you're dealing with grains with similar extract potential, but once you start throwing sugar into the mix, combined with different brewhouse efficiencies, things can get out of line quickly.
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