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Comprehensive Income - Tax Amounts Allocated to Components of Other Comprehensive Loss (Details) - USD ($)
$ in Millions
 3 Months Ended
Nov. 30, 2023
Nov. 30, 2022
Accumulated Other Comprehensive Income (Loss) [Line Items]    
Other comprehensive (loss) income, before tax $ (1.3) $ 0.0
Other comprehensive (loss) income, tax (expense) benefit (0.2) (0.4)
Other comprehensive loss items, net of tax (1.5) (0.4)
Foreign currency translation adjustments    
Accumulated Other Comprehensive Income (Loss) [Line Items]    
Other comprehensive (loss) income, before tax (2.1) (1.5)
Other comprehensive (loss) income, tax (expense) benefit 0.0 0.0
Other comprehensive loss items, net of tax (2.1) (1.5)
Prior service cost    
Accumulated Other Comprehensive Income (Loss) [Line Items]    
Amortization of defined benefit pension items, before tax 0.0 0.7
Amortization of defined benefit pension items, tax (expense) benefit 0.0 (0.2)
Amortization of defined benefit pension items, net of tax 0.0 0.5
Actuarial losses    
Accumulated Other Comprehensive Income (Loss) [Line Items]    
Amortization of defined benefit pension items, before tax 0.8 0.8
Amortization of defined benefit pension items, tax (expense) benefit (0.2) (0.2)
Amortization of defined benefit pension items, net of tax 0.6 0.6
Total defined benefit pension plans, net    
Accumulated Other Comprehensive Income (Loss) [Line Items]    
Other comprehensive (loss) income, before tax 0.8 1.5
Other comprehensive (loss) income, tax (expense) benefit (0.2) (0.4)
Other comprehensive loss items, net of tax $ 0.6 $ 1.1