Income Taxes (Summary of Tax Impact) (Details) - USD ($) $ in Millions	12 Months Ended	24 Months Ended
Aug. 31, 2019	Aug. 31, 2018	Aug. 31, 2019
Income Tax Disclosure [Abstract]
One-time transition tax, inclusive of unrecognized tax benefits		$ 65.9
Re-measurement of the Company's U.S. deferred tax attributes		(10.5)
Change in indefinite reinvestment assertion		85.0
Other		1.9
Income tax expense (benefit)		$ 142.3
One-time transition tax, inclusive of unrecognized tax benefits	$ (19.7)		$ 46.2
Re-measurement of the Company's U.S. deferred tax attributes	1.6		(8.9)
Change in indefinite reinvestment assertion	0.0		85.0
Other	(0.3)		1.6
Income tax expense (benefit)	$ (18.4)		$ 123.9

Tax Cuts And Jobs Act, Incomplete Accounting, Other, Provisional Income Tax Expense (Benefit)

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Tax Cuts And Jobs Act Of 2017, Incomplete Accounting, Undistributed Accumulated Earnings of Foreign Subsidiary, Provisional Income Tax Expense (Benefit)

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Tax Cuts And Jobs Act Of 2017, Undistributed Accumulated Earnings Of Foreign Subsidiary, Provisional Income Tax Expense (Benefit)

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Tax Cuts And Jobs Act, Other, Provisional Income Tax Expense (Benefit)

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Amount of income tax expense (benefit) for remeasurement of deferred tax from change in tax rate pursuant to Tax Cuts and Jobs Act.

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-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
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-Section 50
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Amount of income tax expense (benefit) from effect of Tax Cuts and Jobs Act.

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Amount of reasonable estimate for income tax expense (benefit) for which accounting for tax effect for remeasurement of deferred tax from change in tax rate is incomplete pursuant to Tax Cuts and Jobs Act.

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-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section S99
-Paragraph 2A
-Subparagraph (SAB Topic 5.EE.Q2(b))
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Amount of reasonable estimate for income tax expense (benefit) for which accounting for tax effect is incomplete pursuant to Tax Cuts and Jobs Act.

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-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section S99
-Paragraph 2A
-Subparagraph (SAB Topic 5.EE.Q2(b))
-URI http://asc.fasb.org/extlink&oid=116825942&loc=SL116722634-122817

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Amount of reasonable estimate for income tax expense for which accounting for tax effect from transition tax on accumulated earnings of controlled foreign corporation deemed repatriated is incomplete pursuant to Tax Cuts and Jobs Act.

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Amount of income tax expense from transition tax on accumulated earnings of controlled foreign corporation deemed repatriated pursuant to Tax Cuts and Jobs Act.

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