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Earnings Per Share - Basic and Diluted Earnings per Share, Treasury Stock Method (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	3 Months Ended
	Nov. 30, 2019	Nov. 30, 2018
Earnings Per Share [Abstract]
Net income	$ 57.0	$ 79.6
Basic weighted average shares outstanding (in shares)	39.5	40.0
Common stock equivalents (in shares)	0.1	0.1
Diluted weighted average shares outstanding (in shares)	39.6	40.1
Basic earnings per share (in dollars per share)	$ 1.44	$ 1.99
Diluted earnings per share (in dollars per share)	$ 1.44	$ 1.98

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The amount of net income (loss) from continuing operations per each share of common stock or unit outstanding during the reporting period.

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