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Changes in Stockholders' Equity (Details) - USD ($)
$ / shares in Units, shares in Millions, $ in Millions
 3 Months Ended 9 Months Ended
May 31, 2020
Feb. 29, 2020
Nov. 30, 2019
May 31, 2019
Feb. 28, 2019
Nov. 30, 2018
May 31, 2020
May 31, 2019
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance $ 2,045.1 $ 1,987.3 $ 1,918.9 $ 1,801.8 $ 1,750.9 $ 1,716.8 $ 1,918.9 $ 1,716.8
Net income 60.4 57.2 57.0 88.4 66.3 79.6 174.6 234.3
Other comprehensive income (loss) (12.0) (2.0) 3.8 (7.4) 6.3 (6.2) (10.2) (7.3)
Share-based payment amortization, issuances, and cancellations 7.2 7.5 12.6 7.0 7.1 3.8    
Employee stock purchase plan issuances 0.2 0.2 0.2 0.2 0.2 0.1    
Cash dividends of $0.13 per share paid on common stock (5.2) (5.2) (5.2) (5.1) (5.3) (5.2)    
Stock options exercised   0.1            
Repurchases of common stock         (23.7) (25.0)    
Ending balance $ 2,095.7 $ 2,045.1 $ 1,987.3 $ 1,884.9 $ 1,801.8 $ 1,750.9 2,095.7 1,884.9
Cash dividends paid (usd per share) $ 0.13 $ 0.13 $ 0.13 $ 0.13 $ 0.13 $ 0.13    
Common Stock Outstanding                
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5
Beginning balance (shares) 39.5 39.5 39.5 39.7 39.9 40.0 39.5 40.0
Share-based payment amortization, issuances, and cancellations (shares) 0.0 0.0 0.0 0.0 0.0 0.1    
Repurchases of common stock (shares)         (0.2) (0.2)    
Ending balance $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5 $ 0.5
Ending balance (shares) 39.5 39.5 39.5 39.7 39.7 39.9 39.5 39.7
Paid-in Capital                
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance $ 950.6 $ 942.8 $ 930.0 $ 917.5 $ 910.2 $ 906.3 $ 930.0 $ 906.3
Share-based payment amortization, issuances, and cancellations 7.2 7.5 12.6 7.0 7.1 3.8    
Employee stock purchase plan issuances 0.2 0.2 0.2 0.2 0.2 0.1    
Stock options exercised   0.1            
Ending balance 958.0 950.6 942.8 924.7 917.5 910.2 958.0 924.7
Retained Earnings                
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance 2,399.6 2,347.6 2,295.8 2,121.6 2,060.6 1,999.2 2,295.8 1,999.2
Net income 60.4 57.2 57.0 88.4 66.3 79.6    
Cash dividends of $0.13 per share paid on common stock (5.2) (5.2) (5.2) (5.1) (5.3) (5.2)    
Ending balance 2,454.8 2,399.6 2,347.6 2,204.9 2,121.6 2,060.6 2,454.8 2,204.9
Accumulated Other Comprehensive Loss                
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance (149.6) (147.6) (151.4) (114.7) (121.0) (114.8) (151.4) (114.8)
Other comprehensive income (loss) (12.0) (2.0) 3.8 (7.4) 6.3 (6.2)    
Ending balance (161.6) (149.6) (147.6) (122.1) (114.7) (121.0) (161.6) (122.1)
Treasury Stock, at cost                
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance (1,156.0) (1,156.0) (1,156.0) (1,123.1) (1,099.4) (1,074.4) (1,156.0) (1,074.4)
Repurchases of common stock         (23.7) (25.0)    
Ending balance $ (1,156.0) $ (1,156.0) $ (1,156.0) $ (1,123.1) $ (1,123.1) (1,099.4) $ (1,156.0) (1,123.1)
ASC 606 | ASC 606 adjustments                
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance           (13.0)   (13.0)
ASC 606 | ASC 606 adjustments | Retained Earnings                
Increase (Decrease) in Stockholders' Equity [Roll Forward]                
Beginning balance           $ (13.0)   $ (13.0)