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Comprehensive Income - Schedule of Tax Expense or Benefit Allocated to Each Component of Other Comprehensive Loss (Details) - USD ($)
$ in Millions
 3 Months Ended 9 Months Ended
May 31, 2024
May 31, 2023
May 31, 2024
May 31, 2023
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Other comprehensive (loss) income, before tax $ 1.1 $ 6.7 $ 1.3 $ 6.9
Other comprehensive (loss) income, tax (expense) benefit (0.3) (0.4) (0.6) (1.1)
Other comprehensive income items, net of tax 0.8 6.3 0.7 5.8
Amortization of defined benefit pension items, net of tax     (1.8) (3.2)
Foreign currency translation adjustments        
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Other comprehensive (loss) income, before tax 0.3 5.2 (1.1) 2.6
Other comprehensive (loss) income, tax (expense) benefit 0.0 0.0 0.0 0.0
Other comprehensive income items, net of tax 0.3 5.2 (1.1) 2.6
Amortization of defined benefit pension items, net of tax     0.0 0.0
Total defined benefit pension plans, net        
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Other comprehensive (loss) income, before tax 0.8 1.5 2.4 4.3
Other comprehensive (loss) income, tax (expense) benefit (0.3) (0.4) (0.6) (1.1)
Other comprehensive income items, net of tax 0.5 1.1 1.8 3.2
Amortization of defined benefit pension items, net of tax     (1.8) (3.2)
Prior service cost        
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Amortization of defined benefit pension items, before tax 0.0 0.7 0.0 2.0
Amortization of defined benefit pension items, tax (expense) benefit 0.0 (0.2) 0.0 (0.5)
Amortization of defined benefit pension items, net of tax 0.0 0.5 0.0 1.5
Actuarial losses        
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Amortization of defined benefit pension items, before tax 0.8 0.8 2.4 2.3
Amortization of defined benefit pension items, tax (expense) benefit (0.3) (0.2) (0.6) (0.6)
Amortization of defined benefit pension items, net of tax $ 0.5 $ 0.6 $ 1.8 $ 1.7