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Pension Plans (Details) - Pension Plan - USD ($)
$ in Millions
3 Months Ended
Nov. 30, 2021
Nov. 30, 2020
Defined Benefit Plan, Net Periodic Benefit Cost (Credit) [Abstract]    
Service cost $ 1.2 $ 1.2
Interest cost 1.5 1.6
Expected return on plan assets (3.4) (3.3)
Amortization of prior service cost 0.7 0.7
Recognized actuarial loss 0.9 1.4
Net periodic pension cost $ 0.9 $ 1.6