Income Taxes (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	May 31, 2024	May 31, 2023	May 31, 2024	May 31, 2023	Aug. 31, 2023
Income Tax Disclosure [Abstract]
Effective Income Tax Rate Reconciliation, Percent	4.10%	1.90%	2.10%	3.90%
Unrecognized Tax Benefits that Would Impact Effective Tax Rate	$ 50.1		$ 50.1		$ 116.0