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New Accounting Pronouncements - Effects of Adoption of ASC 606 on Consolidated Balance Sheets (Details) - USD ($)
$ in Millions
May 31, 2019
Aug. 31, 2018
New Accounting Pronouncements or Change in Accounting Principle [Line Items]    
Accounts receivable, net $ 586.0 $ 637.9
Prepayments and other current assets 69.0 32.3
Other accrued liabilities 176.7 164.2
Deferred income tax liabilities 89.6 92.5
Other long-term liabilities 98.7 67.9
Retained earnings 2,204.9 $ 1,999.2
Without ASC 606 Adoption | ASC 606    
New Accounting Pronouncements or Change in Accounting Principle [Line Items]    
Accounts receivable, net 564.7  
Prepayments and other current assets 53.7  
Other accrued liabilities 139.8  
Deferred income tax liabilities 94.8  
Other long-term liabilities 77.8  
Retained earnings 2,220.9  
Higher (Lower) | ASC 606    
New Accounting Pronouncements or Change in Accounting Principle [Line Items]    
Accounts receivable, net 21.3  
Prepayments and other current assets 15.3  
Other accrued liabilities 36.9  
Deferred income tax liabilities (5.2)  
Other long-term liabilities 20.9  
Retained earnings $ (16.0)