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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, 2021	May 31, 2020	May 31, 2021	May 31, 2020
Accumulated Other Comprehensive Income (Loss) [Line Items]
Other comprehensive income (loss), before tax	$ 24.5	$ (11.4)	$ 39.9	$ (8.4)
Other comprehensive income (loss), tax	(3.8)	(0.6)	(4.6)	(1.8)
Other comprehensive income (loss) items, net of tax	20.7	(12.0)	35.3	(10.2)
Foreign currency translation adjustments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Other comprehensive income (loss), before tax	22.3	(13.8)	33.6	(15.6)
Other comprehensive income (loss), tax	0.0	0.0	0.0	0.0
Other comprehensive income (loss) items, net of tax	22.3	(13.8)	33.6	(15.6)
Tax adjustments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Tax adjustments, before tax	0.0	0.0	0.0	0.0
Tax adjustments, tax	(3.2)	0.0	(3.2)	0.0
Tax adjustments, after tax	(3.2)	0.0	(3.2)	0.0
Prior service cost
Accumulated Other Comprehensive Income (Loss) [Line Items]
Amortization of defined benefit pension items, before tax	0.8	1.0	2.2	3.0
Amortization of defined benefit pension items, tax	(0.2)	(0.2)	(0.5)	(0.7)
Amortization of defined benefit pension items, after tax	0.6	0.8	1.7	2.3
Actuarial losses
Accumulated Other Comprehensive Income (Loss) [Line Items]
Amortization of defined benefit pension items, before tax	1.4	1.4	4.1	4.2
Amortization of defined benefit pension items, tax	(0.4)	(0.4)	(0.9)	(1.1)
Amortization of defined benefit pension items, after tax	1.0	1.0	3.2	3.1
Total defined benefit pension plans, net
Accumulated Other Comprehensive Income (Loss) [Line Items]
Other comprehensive income (loss), before tax	2.2	2.4	6.3	7.2
Other comprehensive income (loss), tax	(3.8)	(0.6)	(4.6)	(1.8)
Other comprehensive income (loss) items, net of tax	$ (1.6)	$ 1.8	$ 1.7	$ 5.4

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