How does one see the uptime for a database?

Look at the following SQL query:

SELECT to_char(startup_time,'DD-MON-YYYY HH24:MI:SS') "DB Startup Time"
FROM sys.v_$instance;
or
SELECT to_char(logon_time,'Dy dd Mon HH24:MI:SS') "DB Startup Time"
FROM sys.v_$session
WHERE sid=1 /* this is pmon */
/
or
Check on operating system level when the PMON process was stated (UNIX/ LINUX only):
ps -ef grep pmon

Users still running on Oracle 7 can try one of the following queries:

column STARTED format a18 head 'STARTUP TIME'
select C.INSTANCE,
to_date(JUL.VALUE, 'J')
to_char(floor(SEC.VALUE/3600), '09' )
':'
-- substr (to_char(mod(SEC.VALUE/60, 60), '09'), 2, 2)
substr (to_char(floor(mod(SEC.VALUE/60, 60)), '09'), 2, 2)
'.'
substr (to_char(mod(SEC.VALUE, 60), '09'), 2, 2) STARTED
from SYS.V_$INSTANCE JUL,
SYS.V_$INSTANCE SEC,
SYS.V_$THREAD C
where JUL.KEY like '%JULIAN%'
and SEC.KEY like '%SECOND%';

select to_date(JUL.VALUE, 'J')
to_char(to_date(SEC.VALUE, 'SSSSS'), ' HH24:MI:SS') STARTED
from SYS.V_$INSTANCE JUL,
SYS.V_$INSTANCE SEC
where JUL.KEY like '%JULIAN%'
and SEC.KEY like '%SECOND%';
select to_char(to_date(JUL.VALUE, 'J') + (SEC.VALUE/86400), -- Return a DATE
'DD-MON-YY HH24:MI:SS') STARTED
from V$INSTANCE JUL,
V$INSTANCE SEC
where JUL.KEY like '%JULIAN%'
and SEC.KEY like '%SECOND%';