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Significant Accounting Policies - Selling, Distribution and Administrative Expenses (Details) - USD ($)
$ in Millions
12 Months Ended
Aug. 31, 2019
Aug. 31, 2018
Aug. 31, 2017
Accounting Policies [Abstract]      
Other shipping and handling costs $ 138.4 $ 154.9 $ 138.3
Share-based Payment Arrangement, Noncash Expense [Abstract]      
Share-based payment expense 29.2 32.3 32.0
Income tax benefit for share-based compensation 6.5 8.4 11.1
Net excess tax expense (benefit) related to share-based payment cost 1.6 0.8 (5.2)
Research and development expense 74.7 63.9 52.0
Advertising costs $ 18.5 $ 20.6 $ 18.6