Common Stock and Earnings Per Share - Shares of Common Stock Outstanding (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Feb. 29, 2020	Feb. 28, 2019	Feb. 29, 2020	Feb. 28, 2019
Schedule of Common Stock Outstanding [Roll Forward]
Balance (in shares)			38,117,840	38,192,000
Common stock issued for employee stock plans (in shares)			348,000	426,000
Repurchase of common stock (in shares)	(267,500)	(214,945)	(610,500)	(489,945)
Balance (in shares)	37,849,247	38,100,000	37,849,247	38,100,000
Shares repurchased from employees (in shares)			6,252	27,852
Cost of shares repurchased from employees			$ 1.6	$ 6.1
Repurchase of common stock from employees
Schedule of Common Stock Outstanding [Roll Forward]
Repurchase of common stock (in shares)			(6,000)	(28,000)
Repurchase of common stock under the share repurchase program
Schedule of Common Stock Outstanding [Roll Forward]
Repurchase of common stock (in shares)			(611,000)	(490,000)