Supplemental Guarantor Condensed Consolidating Financial Statements - Cash Flows (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 31, 2018	Aug. 31, 2017	Aug. 31, 2016
Condensed Financial Statements of Cash Flows
Net cash provided by operating activities	$ 353.2	$ 336.6	$ 387.9
Cash flows from investing activities:
Purchases of property, plant, and equipment	(43.6)	(67.3)	(83.7)
Proceeds from sale of property, plant, and equipment	0.0	5.5	2.2
Investments in subsidiaries	0.0		0.0
Proceeds from sale of investment in unconsolidated affiliate	0.0	13.2	0.0
Acquisitions of businesses and intangible assets	(163.2)	0.0	(623.2)
Proceeds from sale of business	1.1	0.0	0.0
Other investing activities	0.0	(0.2)	0.0
Net cash used for investing activities	(205.7)	(48.8)	(704.7)
Cash flow from financing activities:
Borrowings on credit facility	395.4	0.0	0.0
Repayments of borrowings on credit facility	(395.4)	0.0	0.0
(Repayments) issuances of long-term debt	(0.4)
(Repayments) issuances of long-term debt		1.0	2.5
Proceeds from stock option exercises and other	1.7	3.0	14.2
Repurchases of common stock	(298.4)	(357.9)	0.0
Payments for employee taxes on net settlement of equity awards	(8.2)	(15.2)	(16.6)
Intercompany dividends	0.0
Intercompany capital	0.0		0.0
Dividends paid	(21.4)	(22.7)	(22.9)
Net cash used for financing activities	(326.7)	(391.8)	(22.8)
Effect of exchange rate changes on cash	(2.8)	1.9	(4.0)
Net change in cash and cash equivalents	(182.0)	(102.1)	(343.6)
Cash and cash equivalents at beginning of year	311.1	413.2	756.8
Cash and cash equivalents at end of year	129.1	311.1	413.2
Consolidating Adjustments
Condensed Financial Statements of Cash Flows
Net cash provided by operating activities	(36.8)	0.0	0.0
Cash flows from investing activities:
Purchases of property, plant, and equipment	0.0	0.0	0.0
Proceeds from sale of property, plant, and equipment		0.0	0.0
Investments in subsidiaries	154.7		405.6
Proceeds from sale of investment in unconsolidated affiliate		0.0
Acquisitions of businesses and intangible assets	0.0		0.0
Proceeds from sale of business	0.0
Other investing activities		0.0
Net cash used for investing activities	154.7	0.0	405.6
Cash flow from financing activities:
Borrowings on credit facility	0.0
Repayments of borrowings on credit facility	0.0
(Repayments) issuances of long-term debt	0.0
(Repayments) issuances of long-term debt		0.0	0.0
Proceeds from stock option exercises and other	0.0	0.0	0.0
Repurchases of common stock	0.0	0.0
Payments for employee taxes on net settlement of equity awards	0.0	0.0	0.0
Intercompany dividends	36.8
Intercompany capital	(154.7)		(405.6)
Dividends paid	0.0	0.0	0.0
Net cash used for financing activities	(117.9)	0.0	(405.6)
Effect of exchange rate changes on cash	0.0	0.0	0.0
Net change in cash and cash equivalents	0.0	0.0	0.0
Cash and cash equivalents at beginning of year	0.0	0.0	0.0
Cash and cash equivalents at end of year	0.0	0.0	0.0
Parent
Condensed Financial Statements of Cash Flows
Net cash provided by operating activities	323.8	262.3	319.2
Cash flows from investing activities:
Purchases of property, plant, and equipment	0.0	0.0	0.0
Proceeds from sale of property, plant, and equipment		0.0	0.0
Investments in subsidiaries	(154.7)		(405.6)
Proceeds from sale of investment in unconsolidated affiliate		0.0
Acquisitions of businesses and intangible assets	0.0		0.0
Proceeds from sale of business	0.0
Other investing activities		0.0
Net cash used for investing activities	(154.7)	0.0	(405.6)
Cash flow from financing activities:
Borrowings on credit facility	0.0
Repayments of borrowings on credit facility	0.0
(Repayments) issuances of long-term debt	0.0
(Repayments) issuances of long-term debt		0.0	0.0
Proceeds from stock option exercises and other	1.7	3.0	14.2
Repurchases of common stock	(298.4)	(357.9)
Payments for employee taxes on net settlement of equity awards	(8.2)	(15.2)	(16.6)
Intercompany dividends	0.0
Intercompany capital	0.0		0.0
Dividends paid	(21.4)	(22.7)	(22.9)
Net cash used for financing activities	(326.3)	(392.8)	(25.3)
Effect of exchange rate changes on cash	0.0	0.0	0.0
Net change in cash and cash equivalents	(157.2)	(130.5)	(111.7)
Cash and cash equivalents at beginning of year	237.7	368.2	479.9
Cash and cash equivalents at end of year	80.5	237.7	368.2
Subsidiary Guarantor
Condensed Financial Statements of Cash Flows
Net cash provided by operating activities	0.0	0.0	0.0
Cash flows from investing activities:
Purchases of property, plant, and equipment	0.0	0.0	0.0
Proceeds from sale of property, plant, and equipment		0.0	0.0
Investments in subsidiaries	0.0		0.0
Proceeds from sale of investment in unconsolidated affiliate		0.0
Acquisitions of businesses and intangible assets	0.0		0.0
Proceeds from sale of business	0.0
Other investing activities		0.0
Net cash used for investing activities	0.0	0.0	0.0
Cash flow from financing activities:
Borrowings on credit facility	0.0
Repayments of borrowings on credit facility	0.0
(Repayments) issuances of long-term debt	0.0
(Repayments) issuances of long-term debt		0.0	0.0
Proceeds from stock option exercises and other	0.0	0.0	0.0
Repurchases of common stock	0.0	0.0
Payments for employee taxes on net settlement of equity awards	0.0	0.0	0.0
Intercompany dividends	0.0
Intercompany capital	0.0		0.0
Dividends paid	0.0	0.0	0.0
Net cash used for financing activities	0.0	0.0	0.0
Effect of exchange rate changes on cash	0.0	0.0	0.0
Net change in cash and cash equivalents	0.0	0.0	0.0
Cash and cash equivalents at beginning of year	0.0	0.0	0.0
Cash and cash equivalents at end of year	0.0	0.0	0.0
Non- Guarantors
Condensed Financial Statements of Cash Flows
Net cash provided by operating activities	36.0	32.9	13.9
Cash flows from investing activities:
Purchases of property, plant, and equipment	(12.2)	(14.2)	(16.6)
Proceeds from sale of property, plant, and equipment		5.3	2.0
Investments in subsidiaries	0.0		0.0
Proceeds from sale of investment in unconsolidated affiliate		0.0
Acquisitions of businesses and intangible assets	(26.9)		(229.3)
Proceeds from sale of business	1.1
Other investing activities		0.0
Net cash used for investing activities	(38.0)	(8.9)	(243.9)
Cash flow from financing activities:
Borrowings on credit facility	0.0
Repayments of borrowings on credit facility	0.0
(Repayments) issuances of long-term debt	(0.4)
(Repayments) issuances of long-term debt		1.0	2.5
Proceeds from stock option exercises and other	0.0	0.0	0.0
Repurchases of common stock	0.0	0.0
Payments for employee taxes on net settlement of equity awards	0.0	0.0	0.0
Intercompany dividends	(36.8)
Intercompany capital	18.1		0.0
Dividends paid	0.0	0.0	0.0
Net cash used for financing activities	(19.1)	1.0	2.5
Effect of exchange rate changes on cash	(3.7)	3.4	(4.4)
Net change in cash and cash equivalents	(24.8)	28.4	(231.9)
Cash and cash equivalents at beginning of year	73.4	45.0	276.9
Cash and cash equivalents at end of year	48.6	73.4	45.0
Subsidiary Issuer
Condensed Financial Statements of Cash Flows
Net cash provided by operating activities	30.2	41.4	54.8
Cash flows from investing activities:
Purchases of property, plant, and equipment	(31.4)	(53.1)	(67.1)
Proceeds from sale of property, plant, and equipment		0.2	0.2
Investments in subsidiaries	0.0		0.0
Proceeds from sale of investment in unconsolidated affiliate		13.2
Acquisitions of businesses and intangible assets	(136.3)		(393.9)
Proceeds from sale of business	0.0
Other investing activities		(0.2)
Net cash used for investing activities	(167.7)	(39.9)	(460.8)
Cash flow from financing activities:
Borrowings on credit facility	395.4
Repayments of borrowings on credit facility	(395.4)
(Repayments) issuances of long-term debt	0.0
(Repayments) issuances of long-term debt		0.0	0.0
Proceeds from stock option exercises and other	0.0	0.0	0.0
Repurchases of common stock	0.0	0.0
Payments for employee taxes on net settlement of equity awards	0.0	0.0	0.0
Intercompany dividends	0.0
Intercompany capital	136.6		405.6
Dividends paid	0.0	0.0	0.0
Net cash used for financing activities	136.6	0.0	405.6
Effect of exchange rate changes on cash	0.9	(1.5)	0.4
Net change in cash and cash equivalents	0.0	0.0	0.0
Cash and cash equivalents at beginning of year	0.0	0.0	0.0
Cash and cash equivalents at end of year	$ 0.0	$ 0.0	$ 0.0