Income Taxes (Reconciliation of Income Tax Rate) (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Aug. 31, 2020	Aug. 31, 2019	Aug. 31, 2018
Income Tax Disclosure [Abstract]
U.S. federal statutory income tax rate	21.00%	21.00%	25.70%
State income taxes, net of federal tax benefit	(2.60%)	(1.70%)	(1.50%)
Impact of foreign tax rates	(0.90%)	(9.90%)	(19.30%)
Permanent impact of non-deductible cost	3.20%	1.80%	5.90%
Income tax credits	(2.50%)	(3.10%)	(2.80%)
Changes in tax rates on deferred tax assets and liabilities	10.30%	0.20%	4.00%
One-time transition tax related to the Tax Act	0	(0.005)	0.622
Indefinite reinvestment assertion impact	0.00%	0.90%	5.80%
Valuation allowance	16.80%	1.30%	(16.40%)
Non-deductible equity compensation	2.20%	1.40%	5.50%
Impact of intercompany charges and dividends	15.00%	10.40%	7.30%
Reclassification of stranded tax effects in AOCI	0.00%	0.00%	(4.00%)
Global Intangible Low-Taxed Income	13.70%	10.40%	0.00%
Other, net	2.00%	3.60%	4.20%
Effective income tax rate	78.20%	35.80%	76.60%
Income tax benefit on income from subsidiaries	$ 42.6	$ 67.3	$ 52.1
Per basic share income tax benefit on income from subsidiaries (in dollars per share)	$ 0.28	$ 0.43	$ 0.30
Income tax expense associated with remeasurement of referred tax assets	$ 21.2
Reversal of valuation allowance		$ 17.5