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Income Taxes - Schedule of Reconciliation of Federal Statutory Rate to Total Provision for Income Taxes (Details) - USD ($)
$ in Millions
12 Months Ended
Aug. 31, 2021
Aug. 31, 2020
Aug. 31, 2019
Income Tax Disclosure [Abstract]      
Federal income tax computed at statutory rate $ 83.2 $ 68.2 $ 89.2
State income tax, net of federal income tax benefit 10.7 9.7 12.2
Foreign permanent differences and rate differential 2.4 2.4 2.1
Discrete income tax benefits of the U.S. Tax Cuts and Jobs Act 0.0 0.0 (2.2)
Research and development tax credits (7.6) (7.1) (18.1)
Unrecognized tax benefits 0.7 1.8 12.2
Other, net 0.5 1.4 (0.9)
Total provision for income taxes $ 89.9 $ 76.4 $ 94.5