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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, 2019	Feb. 28, 2019	Nov. 30, 2018	May 31, 2018	Feb. 28, 2018	Nov. 30, 2017	May 31, 2019	May 31, 2018	Sep. 01, 2018
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 1,801.8	$ 1,750.9	$ 1,716.8	$ 1,635.8	$ 1,726.1	$ 1,665.6	$ 1,716.8	$ 1,665.6
Net income	88.4	66.3	79.6	73.0	96.9	71.5	234.3	241.4
Other comprehensive income (loss)	(7.4)	6.3	(6.2)	(5.7)	4.3	(8.9)
Reclassification of stranded tax effects of the TCJA					0.0
Amortization, issuance, and cancellations of restricted stock grants	7.0	7.1	3.8	6.5	7.6	2.6
Employee stock purchase plan issuances	0.2	0.2	0.1	0.2	0.1	0.2
Cash dividends of $0.13 per share paid on common stock	(5.1)	(5.3)	(5.2)	(5.3)	(5.4)	(5.5)
Stock options exercised					0.5	0.6
Repurchases of common stock		(23.7)	(25.0)	(104.1)	(194.3)
Ending balance	$ 1,884.9	$ 1,801.8	$ 1,750.9	$ 1,600.4	$ 1,635.8	$ 1,726.1	1,884.9	1,600.4
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)	39.7	39.9	40.0	40.8	41.9	41.8	40.0	41.8
Amortization, issuance, and cancellations of restricted stock grants (shares)	0.0	0.0	0.1	0.0	0.1	0.1
Repurchases of common stock (shares)		(0.2)	(0.2)	(0.8)	(1.2)
Ending balance	$ 0.5	$ 0.5	$ 0.5	$ 0.5	$ 0.5	$ 0.5	$ 0.5	$ 0.5
Ending balance (shares)	39.7	39.7	39.9	40.0	40.8	41.9	39.7	40.0
Paid-in Capital
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 917.5	$ 910.2	$ 906.3	$ 892.5	$ 884.3	$ 881.0	$ 906.3	$ 881.0
Amortization, issuance, and cancellations of restricted stock grants	7.0	7.1	3.8	6.5	7.6	2.5
Employee stock purchase plan issuances	0.2	0.2	0.1	0.2	0.1	0.2
Stock options exercised					0.5	0.6
Ending balance	924.7	917.5	910.2	899.2	892.5	884.3	924.7	899.2
Retained Earnings
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	2,121.6	2,060.6	1,999.2	1,828.5	1,725.9	1,659.9	1,999.2	1,659.9
Net income	88.4	66.3	79.6	73.0	96.9	71.5
Reclassification of stranded tax effects of the TCJA					11.1
Cash dividends of $0.13 per share paid on common stock	(5.1)	(5.3)	(5.2)	(5.3)	(5.4)	(5.5)
Ending balance	2,204.9	2,121.6	2,060.6	1,896.2	1,828.5	1,725.9	2,204.9	1,896.2
Accumulated Other Comprehensive Loss
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(114.7)	(121.0)	(114.8)	(115.4)	(108.6)	(99.7)	(114.8)	(99.7)
Other comprehensive income (loss)	(7.4)	6.3	(6.2)	(5.7)	4.3	(8.9)	(7.3)	(10.3)
Reclassification of stranded tax effects of the TCJA					(11.1)			(11.1)
Ending balance	(122.1)	(114.7)	(121.0)	(121.1)	(115.4)	(108.6)	(122.1)	(121.1)
Treasury Stock, at cost
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(1,123.1)	(1,099.4)	(1,074.4)	(970.3)	(776.0)	(776.1)	(1,074.4)	(776.1)
Amortization, issuance, and cancellations of restricted stock grants						0.1
Repurchases of common stock		(23.7)	(25.0)	(104.1)	(194.3)
Ending balance	$ (1,123.1)	$ (1,123.1)	$ (1,099.4)	$ (1,074.4)	$ (970.3)	$ (776.0)	$ (1,123.1)	$ (1,074.4)
ASC 606
Increase (Decrease) in Stockholders' Equity [Roll Forward]
ASC 606 adjustments									$ (13.0)
ASC 606 | Retained Earnings
Increase (Decrease) in Stockholders' Equity [Roll Forward]
ASC 606 adjustments									$ (13.0)

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