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Income Taxes (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
May 31, 2023
May 31, 2022
May 31, 2023
May 31, 2022
Aug. 31, 2022
Income Tax Disclosure [Abstract]          
Effective Income Tax Rate Reconciliation, Percent 1.90% 9.80% 3.90% 6.70%  
Unrecognized Tax Benefits that Would Impact Effective Tax Rate $ 115.7   $ 115.7   $ 115.1