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Comprehensive Income - Tax Amounts Allocated to Components of Other Comprehensive Income (Loss) (Details) - USD ($)
$ in Millions
 3 Months Ended 9 Months Ended
May 31, 2022
May 31, 2021
May 31, 2022
May 31, 2021
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Other comprehensive (loss) income, before tax $ (0.3) $ 24.5 $ (4.2) $ 39.9
Other comprehensive (loss) income, tax (0.3) (3.8) (1.1) (4.6)
Other comprehensive (loss) income items, net of tax (0.6) 20.7 (5.3) 35.3
Foreign currency translation adjustments        
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Other comprehensive (loss) income, before tax (1.8) 22.3 (8.9) 33.6
Other comprehensive (loss) income, tax 0.0 0.0 0.0 0.0
Other comprehensive (loss) income items, net of tax (1.8) 22.3 (8.9) 33.6
Prior service cost        
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Amortization of defined benefit pension items, before tax 0.7 0.8 2.1 2.2
Amortization of defined benefit pension items, tax (0.1) (0.2) (0.5) (0.5)
Amortization of defined benefit pension items, after tax 0.6 0.6 1.6 1.7
Actuarial losses        
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Amortization of defined benefit pension items, before tax 0.8 1.4 2.6 4.1
Amortization of defined benefit pension items, tax (0.2) (0.4) (0.6) (0.9)
Amortization of defined benefit pension items, after tax 0.6 1.0 2.0 3.2
Total defined benefit pension plans, net        
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Other comprehensive (loss) income, before tax 1.5 2.2 4.7 6.3
Other comprehensive (loss) income, tax (0.3) (3.8) (1.1) (4.6)
Other comprehensive (loss) income items, net of tax 1.2 (1.6) 3.6 1.7
Tax adjustments        
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Tax adjustments, before tax 0.0 0.0 0.0 0.0
Tax adjustments, tax 0.0 (3.2) 0.0 (3.2)
Tax adjustments, after tax $ 0.0 $ (3.2) $ 0.0 $ (3.2)