What does a "Buffer cache hit ratio" of 9990 mean?
Confusing, right?

Well, to actually get the ratio, you'll need to do it yourself using the Buffer cache hit ratio base in addition to the Buffer cache hit ratio by taking the result from Buffer cache hit ratio / Buffer cache hit ratio base.

Try the below query (from Less Than Dot), which should give you the % you're looking for:

SELECT (a.cntr_value * 1.0 / b.cntr_value) * 100.0 as BufferCacheHitRatio
FROM sys.dm_os_performance_counters  a
JOIN  (SELECT cntr_value, OBJECT_NAME 
    FROM sys.dm_os_performance_counters  
    WHERE counter_name = 'Buffer cache hit ratio base'
        AND OBJECT_NAME = 'SQLServer:Buffer Manager') b ON  a.OBJECT_NAME = b.OBJECT_NAME
WHERE a.counter_name = 'Buffer cache hit ratio'
AND a.OBJECT_NAME = 'SQLServer:Buffer Manager'