I think something like this should be more like it:
-- [params]
-- date :start_date
-- date :end_date
WITH results AS (
SELECT LOWER(term) AS term,
COUNT(*) AS searches,
SUM(CASE WHEN search_result_id IS NOT NULL THEN 1 ELSE 0 END) AS click_through
FROM search_logs
WHERE created_at BETWEEN :start_date AND :end_date
GROUP BY term
)
SELECT term AS "Search Term",
searches AS "Searches",
click_through AS "Clicks-Through",
CEIL ((click_through/searches::float) * 100) || '%' AS "CTR"
FROM results
ORDER BY searches DESC
Hopefully that helps, but let me know if you want any tweaks.