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New Accounting Pronouncements - Effects of Adoption of ASC 606 on Consolidated Statement of Comprehensive Income (Details) - USD ($)
$ / shares in Units, $ in Millions
 3 Months Ended
Nov. 30, 2018
Nov. 30, 2017
New Accounting Pronouncements or Change in Accounting Principle [Line Items]    
Net sales $ 932.6 $ 842.8
Cost of products sold 565.1 492.9
Selling, distribution, and administrative expenses 250.1 229.5
Operating profit 116.4 120.2
Income tax expense 26.8 39.4
Net income $ 79.6 $ 71.5
Basic earnings per share (in dollars per share) $ 1.99 $ 1.71
Diluted earnings per share (in dollars per share) $ 1.98 $ 1.70
Without ASC 606 Adoption | ASC 606    
New Accounting Pronouncements or Change in Accounting Principle [Line Items]    
Net sales $ 935.0  
Cost of products sold 566.4  
Selling, distribution, and administrative expenses 250.0  
Operating profit 117.6  
Income tax expense 27.1  
Net income $ 80.5  
Basic earnings per share (in dollars per share) $ 2.01  
Diluted earnings per share (in dollars per share) $ 2.00  
Higher (Lower) | ASC 606    
New Accounting Pronouncements or Change in Accounting Principle [Line Items]    
Net sales $ (2.4)  
Cost of products sold (1.3)  
Selling, distribution, and administrative expenses 0.1  
Operating profit (1.2)  
Income tax expense (0.3)  
Net income $ (0.9)  
Basic earnings per share (in dollars per share) $ (0.02)  
Diluted earnings per share (in dollars per share) $ (0.02)