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Income Taxes (Reconciliation of Income Tax Rate) (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Aug. 31, 2019	Aug. 31, 2018	Aug. 31, 2017
Income Tax Disclosure [Abstract]
U.S. federal statutory income tax rate	21.00%	25.70%	35.00%
State income taxes, net of federal tax benefit	(1.70%)	(1.50%)	(3.30%)
Impact of foreign tax rates	(9.90%)	(19.30%)	(42.70%)
Permanent impact of non-deductible cost	1.80%	5.90%	2.90%
Income tax credits	(3.10%)	(2.80%)	(6.30%)
Changes in tax rates on deferred tax assets and liabilities	0.20%	4.00%	0.30%
One-time transition tax related to the Tax Act	(0.005)	0.622	0.000
Indefinite reinvestment assertion impact	0.90%	5.80%	0.00%
Valuation allowance	1.30%	(16.40%)	14.80%
Non-deductible equity compensation	1.40%	5.50%	4.50%
Impact of intercompany charges and dividends	10.40%	7.30%	38.30%
Reclassification of stranded tax effects in AOCI	(0.00%)	(4.00%)	(0.00%)
Global Intangible Low-Taxed Income	10.40%	0.00%	0.00%
Other, net	3.60%	4.20%	6.90%
Effective income tax rate	35.80%	76.60%	50.40%
Income tax benefit on income from subsidiaries	$ 67.3	$ 52.1	$ 38.6
Per basic share income tax benefit on income from subsidiaries (in dollars per share)	$ 0.43	$ 0.30	$ 0.22
Reversal of valuation allowance	$ 17.5

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