While your tag is a WWI type, it was issued between 1919 - 1940.
According to Wikipedia and other sources -
between 1919 and 1940 the numbers ranged from 6 000 000 to 7 099 999
After 1940, Latimer likely got a new 8 digit service number.
I think this is your guy:
[TABLE="width: 716"]
[TR]
[TH]Field Title[/TH]
[TH="bgcolor: #EEEEEE"]Value[/TH]
[TH="bgcolor: #EEEEEE"]Meaning[/TH]
[/TR]
[TR]
[TD="width: 165"]ARMY SERIAL NUMBER[/TD]
[TD]06827207[/TD]
[TD]06827207[/TD]
[/TR]
[TR]
[TD="width: 165"]NAME[/TD]
[TD]LATIMER#HERBERT#S#######[/TD]
[TD]LATIMER#HERBERT#S#######[/TD]
[/TR]
[TR]
[TD="width: 165"]RESIDENCE: STATE[/TD]
[TD]75[/TD]
[TD]MISSOURI[/TD]
[/TR]
[TR]
[TD="width: 165"]RESIDENCE: COUNTY[/TD]
[TD]143[/TD]
[TD]NEW MADRID[/TD]
[/TR]
[TR]
[TD="width: 165"]PLACE OF ENLISTMENT[/TD]
[TD]8888[/TD]
[TD]Undefined Code[/TD]
[/TR]
[TR]
[TD="width: 165"]DATE OF ENLISTMENT DAY[/TD]
[TD]26[/TD]
[TD]26[/TD]
[/TR]
[TR]
[TD="width: 165"]DATE OF ENLISTMENT MONTH[/TD]
[TD]07[/TD]
[TD]07[/TD]
[/TR]
[TR]
[TD="width: 165"]DATE OF ENLISTMENT YEAR[/TD]
[TD]39[/TD]
[TD]39[/TD]
[/TR]
[TR]
[TD="width: 165"]GRADE: ALPHA DESIGNATION[/TD]
[TD]####[/TD]
[TD]Undefined Code[/TD]
[/TR]
[TR]
[TD="width: 165"]GRADE: CODE[/TD]
[TD]#[/TD]
[TD]Undefined Code[/TD]
[/TR]
[TR]
[TD="width: 165"]BRANCH: ALPHA DESIGNATION[/TD]
[TD]###[/TD]
[TD]Undefined Code[/TD]
[/TR]
[TR]
[TD="width: 165"]BRANCH: CODE[/TD]
[TD]08[/TD]
[TD]Detached Enlisted Men's List[/TD]
[/TR]
[TR]
[TD="width: 165"]FIELD USE AS DESIRED[/TD]
[TD]#[/TD]
[TD]#[/TD]
[/TR]
[TR]
[TD="width: 165"]TERM OF ENLISTMENT[/TD]
[TD]0[/TD]
[TD]Undefined Code[/TD]
[/TR]
[TR]
[TD="width: 165"]LONGEVITY[/TD]
[TD]###[/TD]
[TD]###[/TD]
[/TR]
[TR]
[TD="width: 165"]SOURCE OF ARMY PERSONNEL[/TD]
[TD]#[/TD]
[TD]Undefined Code[/TD]
[/TR]
[TR]
[TD="width: 165"]NATIVITY[/TD]
[TD]75[/TD]
[TD]MISSOURI[/TD]
[/TR]
[TR]
[TD="width: 165"]YEAR OF BIRTH[/TD]
[TD]09[/TD]
[TD]09[/TD]
[/TR]
[TR]
[TD="width: 165"]RACE AND CITIZENSHIP[/TD]
[TD]#[/TD]
[TD]Undefined Code[/TD]
[/TR]
[TR]
[TD="width: 165"]EDUCATION[/TD]
[TD]9[/TD]
[TD]Post-graduate[/TD]
[/TR]
[TR]
[TD="width: 165"]CIVILIAN OCCUPATION[/TD]
[TD]889[/TD]
[TD]Undefined Code[/TD]
[/TR]
[TR]
[TD="width: 165"]MARITAL STATUS[/TD]
[TD]0[/TD]
[TD]Undefined Code[/TD]
[/TR]
[TR]
[TD="width: 165"]COMPONENT OF THE ARMY[/TD]
[TD]1[/TD]
[TD]Regular Army (including Officers, Nurses, Warrant Officers, and Enlisted Men)[/TD]
[/TR]
[/TABLE]