To find the percentage of occupancy, we need to first calculate the total number of available bed days from January through June.
Since January, March, May, July, August, October, and December have 31 days each, and April, June, September, and November have 30 days each in a non-leap year, we will have a total of:
31 + 28 + 31 + 30 + 31 + 30 = 181 days in January through June.
The total number of available bed days is calculated by multiplying the number of beds by the number of days in the month:
50 \text{ beds} \times 181 \text{ days} = 9050 \text{ bed days}
Now, we can calculate the occupancy rate by dividing the total inpatient service days by the total available bed days and multiplying by 100 to get a percentage:
\text{Occupancy Rate} = \left(\dfrac{9001}{9050}\right) \times 100 = 99.5\%
Therefore, the hospital's occupancy percentage during January through June was 99.5%.
Answer: The occupancy percentage is 99.5%.