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Supplemental Guarantor Condensed Consolidating Financial Statements (Cash Flows) (Details) - USD ($)
$ in Millions
 3 Months Ended
Nov. 30, 2018
Nov. 30, 2017
Condensed Financial Statements, Captions [Line Items]    
Net cash provided by (used for) operating activities $ 131.8 $ 139.8
Cash flows from investing activities:    
Purchases of property, plant, and equipment (14.0) (10.3)
Other investing activities 2.7 0.0
Net cash used for investing activities (11.3) (10.3)
Cash flows from financing activities:    
Borrowings on credit facility 55.4 0.0
Repayments of borrowings on credit facility (55.4) 0.0
Repayments of long-term debt (0.1) (0.1)
Proceeds from stock option exercises and other 0.1 0.8
Repurchases of common stock (25.0) 0.0
Withholding taxes on net settlement of equity awards (3.9) (6.0)
Dividends paid (5.2) (5.5)
Net cash used for financing activities (34.1) (10.8)
Effect of exchange rates changes on cash (0.7) (1.2)
Net change in cash and cash equivalents 85.7 117.5
Cash and cash equivalents at beginning of period 129.1 311.1
Cash and cash equivalents at end of period 214.8 428.6
Parent    
Condensed Financial Statements, Captions [Line Items]    
Net cash provided by (used for) operating activities 110.9 137.8
Cash flows from investing activities:    
Purchases of property, plant, and equipment 0.0 0.0
Other investing activities 0.6  
Net cash used for investing activities 0.6 0.0
Cash flows from financing activities:    
Borrowings on credit facility 0.0  
Repayments of borrowings on credit facility 0.0  
Repayments of long-term debt 0.0 0.0
Proceeds from stock option exercises and other 0.1 0.8
Repurchases of common stock (25.0)  
Withholding taxes on net settlement of equity awards (3.9) (6.0)
Dividends paid (5.2) (5.5)
Net cash used for financing activities (34.0) (10.7)
Effect of exchange rates changes on cash 0.0 0.0
Net change in cash and cash equivalents 77.5 127.1
Cash and cash equivalents at beginning of period 80.5 237.7
Cash and cash equivalents at end of period 158.0 364.8
Subsidiary Issuer    
Condensed Financial Statements, Captions [Line Items]    
Net cash provided by (used for) operating activities 8.7 5.8
Cash flows from investing activities:    
Purchases of property, plant, and equipment (11.5) (7.2)
Other investing activities 2.1  
Net cash used for investing activities (9.4) (7.2)
Cash flows from financing activities:    
Borrowings on credit facility 55.4  
Repayments of borrowings on credit facility (55.4)  
Repayments of long-term debt 0.0 0.0
Proceeds from stock option exercises and other 0.0 0.0
Repurchases of common stock 0.0  
Withholding taxes on net settlement of equity awards 0.0 0.0
Dividends paid 0.0 0.0
Net cash used for financing activities 0.0 0.0
Effect of exchange rates changes on cash 0.7 1.4
Net change in cash and cash equivalents 0.0 0.0
Cash and cash equivalents at beginning of period 0.0 0.0
Cash and cash equivalents at end of period 0.0 0.0
Subsidiary Guarantor    
Condensed Financial Statements, Captions [Line Items]    
Net cash provided by (used for) operating activities 0.0 0.0
Cash flows from investing activities:    
Purchases of property, plant, and equipment 0.0 0.0
Other investing activities 0.0  
Net cash used for investing activities 0.0 0.0
Cash flows from financing activities:    
Borrowings on credit facility 0.0  
Repayments of borrowings on credit facility 0.0  
Repayments of long-term debt 0.0 0.0
Proceeds from stock option exercises and other 0.0 0.0
Repurchases of common stock 0.0  
Withholding taxes on net settlement of equity awards 0.0 0.0
Dividends paid 0.0 0.0
Net cash used for financing activities 0.0 0.0
Effect of exchange rates changes on cash 0.0 0.0
Net change in cash and cash equivalents 0.0 0.0
Cash and cash equivalents at beginning of period 0.0 0.0
Cash and cash equivalents at end of period 0.0 0.0
Non- Guarantors    
Condensed Financial Statements, Captions [Line Items]    
Net cash provided by (used for) operating activities 12.2 (3.8)
Cash flows from investing activities:    
Purchases of property, plant, and equipment (2.5) (3.1)
Other investing activities 0.0  
Net cash used for investing activities (2.5) (3.1)
Cash flows from financing activities:    
Borrowings on credit facility 0.0  
Repayments of borrowings on credit facility 0.0  
Repayments of long-term debt (0.1) (0.1)
Proceeds from stock option exercises and other 0.0 0.0
Repurchases of common stock 0.0  
Withholding taxes on net settlement of equity awards 0.0 0.0
Dividends paid 0.0 0.0
Net cash used for financing activities (0.1) (0.1)
Effect of exchange rates changes on cash (1.4) (2.6)
Net change in cash and cash equivalents 8.2 (9.6)
Cash and cash equivalents at beginning of period 48.6 73.4
Cash and cash equivalents at end of period 56.8 63.8
Consolidating Adjustments    
Condensed Financial Statements, Captions [Line Items]    
Net cash provided by (used for) operating activities 0.0 0.0
Cash flows from investing activities:    
Purchases of property, plant, and equipment 0.0 0.0
Other investing activities 0.0  
Net cash used for investing activities 0.0 0.0
Cash flows from financing activities:    
Borrowings on credit facility 0.0  
Repayments of borrowings on credit facility 0.0  
Repayments of long-term debt 0.0 0.0
Proceeds from stock option exercises and other 0.0 0.0
Repurchases of common stock 0.0  
Withholding taxes on net settlement of equity awards 0.0 0.0
Dividends paid 0.0 0.0
Net cash used for financing activities 0.0 0.0
Effect of exchange rates changes on cash 0.0 0.0
Net change in cash and cash equivalents 0.0 0.0
Cash and cash equivalents at beginning of period 0.0 0.0
Cash and cash equivalents at end of period $ 0.0 $ 0.0