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Changes in Equity (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	3 Months Ended
	Nov. 30, 2018	Nov. 30, 2017	Sep. 01, 2018	Aug. 31, 2018
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 1,716.8	$ 1,665.6
Net income	79.6	71.5
Other comprehensive loss	(6.2)	(8.9)
Amortization, issuance, and cancellations of restricted stock grants	3.8	2.6
Employee stock purchase plan issuances	0.1	0.2
Cash dividends of $0.13 per share paid on common stock	(5.2)	(5.5)
Stock options exercised		0.6
Repurchases of common stock	(25.0)
Ending balance	$ 1,750.9	$ 1,726.1
Cash dividends paid (usd per share)	$ 0.13	$ 0.13
Common Stock Outstanding
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 0.5	$ 0.5
Beginning balance (shares)	40.0	41.8
Amortization, issuance, and cancellations of restricted stock grants (shares)	0.1	0.1
Repurchases of common stock (shares)	(0.2)
Ending balance	$ 0.5	$ 0.5
Ending balance (shares)	39.9	41.9
Paid-in Capital
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 906.3	$ 881.0
Amortization, issuance, and cancellations of restricted stock grants	3.8	2.5
Employee stock purchase plan issuances	0.1	0.2
Stock options exercised		0.6
Ending balance	910.2	884.3
Retained Earnings
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	1,999.2	1,659.9
Net income	79.6	71.5
Cash dividends of $0.13 per share paid on common stock	(5.2)	(5.5)
Ending balance	2,060.6	1,725.9
Accumulated Other Comprehensive Loss
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(114.8)	(99.7)
Other comprehensive loss	(6.2)	(8.9)
Ending balance	(121.0)	(108.6)
Treasury Stock, at cost
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(1,074.4)	(776.1)
Amortization, issuance, and cancellations of restricted stock grants		0.1
Repurchases of common stock	(25.0)
Ending balance	$ (1,099.4)	$ (776.0)
ASC 606
Increase (Decrease) in Stockholders' Equity [Roll Forward]
ASC 606 adjustments			$ (13.0)	$ (13.0)
ASC 606 \| Retained Earnings
Increase (Decrease) in Stockholders' Equity [Roll Forward]
ASC 606 adjustments				$ (13.0)