Write SQL query to solve given problem: What is the percentage of female clients in the Middle Atlantic?. Keep the solution inside sql tag ```sql [SQL-Query] ```
SELECT CAST(SUM(CASE WHEN T1.sex = 'Female' THEN 1 ELSE 0 END) AS REAL) * 100 / COUNT(T1.sex) FROM client AS T1 INNER JOIN district AS T2 ON T1.district_id = T2.district_id WHERE T2.division = 'South Atlantic'