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Goodwill and Intangible Assets (Changes in Goodwill) (Details) - USD ($)
$ in Millions
9 Months Ended
May 31, 2019
May 31, 2018
Goodwill [Roll Forward]    
Goodwill, Beginning Balance $ 970.6 $ 900.9
Additions from acquired businesses 0.0 75.7
Adjustments to provisional amounts (0.2) 0.0
Foreign currency translation adjustments (6.3) (6.1)
Goodwill, Ending Balance $ 964.1 $ 970.5