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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

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