"on the order of" is not synonymous with "approximately"
"on the order of" 1000000 means any number from 1000001 through 9999999
I would expect "approximately" to mean accurate to within the next order of magnitude down. e.g. I would expect "approximately 500000" to mean a range of 400000 to 600000; maybe 350000 to 650000 if you're stretching it.
