Share-Based Compensation (Narrative) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Feb. 29, 2024	Feb. 28, 2023	Feb. 29, 2024	Feb. 28, 2023
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]
Share-based compensation expense	$ 1.8	$ 1.7	$ 3.5	$ 3.3