Army service numbers - originally called serial numbers - were first issued to enlisted personnel during World War I. The number “1” was assigned to Master Sergeant Arthur B. Crean on 28 February 1918. Crean was Sergeant Major, Headquarters, Allied Expeditionary Forces (AEF) in France. Commissioned officers began receiving numbers in 1920 (number “O1” was assigned to General of the Armies John J. Pershing, Army Chief of Staff). Enlisted service numbers were assigned entirely at random until 1940, by which time numbers had reached the 7 or 8 million (7 000 000 or 8 000 000) series. Commissioned service numbers were assigned according to component and relative rank, officers of the Regular Army having precedence.
All four series of ten-digit numbers reflected enlisted status. Commissioned status was indicated by four- to nine-digit numbers with an “O” prefix. The 10 million (10 000 000) series were members of the Regular Army (i. e., voluntary enlistees), the 20 million series were Army of the United States (AUS) drawn from the National Guard and the 30 & 40 million series were Army of the United States (AUS) inducted through the Selective Service System. As stated, the second character of the ten-digit enlisted service number simply indicates the Selective Service Region - what Berry calls a “state grouping” - from which the individual entered service, whether he enlisted or was inducted.
Army and U. S. Air Force enlisted service numbers followed the same pattern until replaced by Social Security Numbers in July 1969. In 1945, prefixes were introduced to identify an individual's component: RA = Regular Army; NG = National Guard and ER = Enlisted Reserve Corps (draftee). "ER" was later replaced by "US" (Army of the United States). In accordance with the above, service number RA 37 788 990 identifies an individual who was drafted during World War II and re-enlisted in the Regular Army. This individual was inducted somewhere within Selective Service Region Seven (Colorado, Iowa, Kansas, Minnesota, Missouri, Nebraska, North & South Dakota and Wyoming). There's no way to determine the individual's place of birth from the number itself.
It's possible to locate someone's place of birth with identification tags (i. e., the service number on the tag) but it seems like a lot of unnecessary work. Sort of like driving a ten-penny nail with a sledge hammer.