At some point all service numbers became ones social security numbers, which unless my fingers have failed me, have 9 digits. I know this was before 1971, when I entered the AF Reserve as an AFROTC cadet. (ROTC cadets join the reserve, inactive, as E-1, unless they have prior enlisted time, in which case they join at their highest enlisted rank, but they never attend basic training, just the ROTC stuff again unless they already have, the same is true of OTS cadets).
....
Turns out I was half right the changeover to SSN occurred as follows:
Army and Air Force July 1, 1969
Navy and Marine Corps January 1, 1972
Coast Guard October 1, 1974
Roger that..!...Mine was 8 digits for the time period we are concerned with. I punched out in 75 with 9 digits...!