Supplemental Guarantor Condensed Consolidating Financial Statements (Cash Flows) (Details) - USD ($) $ in Millions	6 Months Ended
	Feb. 28, 2019	Feb. 28, 2018
Condensed Financial Statements, Captions [Line Items]
Net cash provided by operating activities	$ 188.3	$ 177.6
Cash flows from investing activities:
Purchases of property, plant, and equipment	(24.9)	(20.9)
Other investing activities	2.9	0.7
Investments in subsidiaries		0.0
Acquisitions of business, net of cash acquired	0.0	(26.4)
Net cash used for investing activities	(22.0)	(46.6)
Cash flows from financing activities:
Borrowings on credit facility	86.5	0.0
Repayments of borrowings on credit facility	(86.5)	0.0
Repayments of long-term debt	(0.2)	(0.2)
Proceeds from stock option exercises and other	0.3	1.4
Repurchases of common stock	(48.7)	(194.3)
Withholding taxes on net settlement of equity awards	(4.3)	(6.7)
Intercompany Capital		0.0
Dividends paid	(10.5)	(10.9)
Net cash used for financing activities	(63.4)	(210.7)
Effect of exchange rates changes on cash	0.0	(1.6)
Net change in cash and cash equivalents	102.9	(81.3)
Cash and cash equivalents at beginning of period	129.1	311.1
Cash and cash equivalents at end of period	232.0	229.8
Parent
Condensed Financial Statements, Captions [Line Items]
Net cash provided by operating activities	133.8	141.1
Cash flows from investing activities:
Purchases of property, plant, and equipment	0.0	0.0
Other investing activities	0.8	0.7
Investments in subsidiaries		(26.4)
Acquisitions of business, net of cash acquired		0.0
Net cash used for investing activities	0.8	(25.7)
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	0.3	1.4
Repurchases of common stock	(48.7)	(194.3)
Withholding taxes on net settlement of equity awards	(4.3)	(6.7)
Intercompany Capital		0.0
Dividends paid	(10.5)	(10.9)
Net cash used for financing activities	(63.2)	(210.5)
Effect of exchange rates changes on cash	0.2	0.0
Net change in cash and cash equivalents	71.6	(95.1)
Cash and cash equivalents at beginning of period	80.5	237.7
Cash and cash equivalents at end of period	152.1	142.6
Subsidiary Issuer
Condensed Financial Statements, Captions [Line Items]
Net cash provided by operating activities	35.9	14.4
Cash flows from investing activities:
Purchases of property, plant, and equipment	(20.2)	(15.2)
Other investing activities	2.1	0.0
Investments in subsidiaries		0.0
Acquisitions of business, net of cash acquired		0.0
Net cash used for investing activities	(18.1)	(15.2)
Cash flows from financing activities:
Borrowings on credit facility	86.5
Repayments of borrowings on credit facility	(86.5)
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	0.0
Withholding taxes on net settlement of equity awards	0.0	0.0
Intercompany Capital		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	0.8
Net change in cash and cash equivalents	17.8	0.0
Cash and cash equivalents at beginning of period	0.0	0.0
Cash and cash equivalents at end of period	17.8	0.0
Subsidiary Guarantor
Condensed Financial Statements, Captions [Line Items]
Net cash provided by 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	0.0
Investments in subsidiaries		0.0
Acquisitions of business, net of cash acquired		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	0.0
Withholding taxes on net settlement of equity awards	0.0	0.0
Intercompany Capital		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 operating activities	18.6	22.1
Cash flows from investing activities:
Purchases of property, plant, and equipment	(4.7)	(5.7)
Other investing activities	0.0	0.0
Investments in subsidiaries		0.0
Acquisitions of business, net of cash acquired		(26.4)
Net cash used for investing activities	(4.7)	(32.1)
Cash flows from financing activities:
Borrowings on credit facility	0.0
Repayments of borrowings on credit facility	0.0
Repayments of long-term debt	(0.2)	(0.2)
Proceeds from stock option exercises and other	0.0	0.0
Repurchases of common stock	0.0	0.0
Withholding taxes on net settlement of equity awards	0.0	0.0
Intercompany Capital		26.4
Dividends paid	0.0	0.0
Net cash used for financing activities	(0.2)	26.2
Effect of exchange rates changes on cash	(0.2)	(2.4)
Net change in cash and cash equivalents	13.5	13.8
Cash and cash equivalents at beginning of period	48.6	73.4
Cash and cash equivalents at end of period	62.1	87.2
Consolidating Adjustments
Condensed Financial Statements, Captions [Line Items]
Net cash provided by 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	0.0
Investments in subsidiaries		26.4
Acquisitions of business, net of cash acquired		0.0
Net cash used for investing activities	0.0	26.4
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	0.0
Withholding taxes on net settlement of equity awards	0.0	0.0
Intercompany Capital		(26.4)
Dividends paid	0.0	0.0
Net cash used for financing activities	0.0	(26.4)
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