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New Accounting Pronouncements - Effects of Adoption of ASC 606 on Consolidated Statement of Comprehensive Income (Details) - USD ($) $ / shares in Units, $ 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
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Net sales	$ 947.6			$ 944.0			$ 2,734.6	$ 2,618.9
Cost of products sold	564.0			554.9			1,649.6	1,545.4
Selling, distribution, and administrative expenses	263.4			271.8			751.1	745.7
Operating profit	120.3			107.4			332.6	317.1
Income tax expense	23.4			26.2			70.1	47.4
Net income	$ 88.4	$ 66.3	$ 79.6	$ 73.0	$ 96.9	$ 71.5	$ 234.3	$ 241.4
Basic earnings per share (in dollars per share)	$ 2.23			$ 1.81			$ 5.89	$ 5.86
Diluted earnings per share (in dollars per share)	$ 2.22			$ 1.80			$ 5.87	$ 5.85
Without ASC 606 Adoption | ASC 606
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Net sales	$ 951.4						$ 2,742.4
Cost of products sold	566.2						1,653.6
Selling, distribution, and administrative expenses	263.4						750.9
Operating profit	121.9						336.6
Income tax expense	23.8						71.1
Net income	$ 89.6						$ 237.3
Basic earnings per share (in dollars per share)	$ 2.26						$ 5.97
Diluted earnings per share (in dollars per share)	$ 2.25						$ 5.95
Higher (Lower) | ASC 606
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Net sales	$ (3.8)						$ (7.8)
Cost of products sold	(2.2)						(4.0)
Selling, distribution, and administrative expenses	0.0						0.2
Operating profit	(1.6)						(4.0)
Income tax expense	(0.4)						(1.0)
Net income	$ (1.2)						$ (3.0)
Basic earnings per share (in dollars per share)	$ (0.03)						$ (0.08)
Diluted earnings per share (in dollars per share)	$ (0.03)						$ (0.08)

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