There you go. You remember when a Mars probe failed because some idiots at NASA used inches&feet instead of centimeters? Cost us taxpayers $300 million.
Arbitrary units?--with this lame argument, you can 'prove' that an inch is a mile; that a kilowatt is a pound; that a calorie is a volt; that blood pressure is miles per gallon.
Your whole post is just silly.
In fairness, it appears that the two numbers are a ratio, so the units cancel. The assertion seems to be that if a specific value were different by one part in 10^120, then life would be impossible. As Ichneumon details in #104 this doesn't prove anything even if true, but it's not unreasonable on its face.
"Arbitrary units" make me think of "pyramid inches".