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New Accounting Pronouncements - Effects of Adoption of ASC 606 on Consolidated Balance Sheets (Details) - USD ($)
$ in Millions
Nov. 30, 2018
Aug. 31, 2018
New Accounting Pronouncements or Change in Accounting Principle [Line Items]    
Accounts receivable, net $ 556.7 $ 637.9
Prepayments and other current assets 60.1 32.3
Other accrued liabilities 222.2 164.2
Deferred income tax liabilities 88.7 92.5
Other long-term liabilities 96.8 67.9
Retained earnings 2,060.6 $ 1,999.2
Without ASC 606 Adoption | ASC 606    
New Accounting Pronouncements or Change in Accounting Principle [Line Items]    
Accounts receivable, net 535.7  
Prepayments and other current assets 43.9  
Other accrued liabilities 184.8  
Deferred income tax liabilities 93.2  
Other long-term liabilities 78.6  
Retained earnings 2,074.5  
Higher (Lower) | ASC 606    
New Accounting Pronouncements or Change in Accounting Principle [Line Items]    
Accounts receivable, net 21.0  
Prepayments and other current assets 16.2  
Other accrued liabilities 37.4  
Deferred income tax liabilities (4.5)  
Other long-term liabilities 18.2  
Retained earnings $ (13.9)