Common Stock and Earnings Per Share - Shares of Common Stock Outstanding (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	May 31, 2020	May 31, 2019	May 31, 2020	May 31, 2019
Schedule of Common Stock Outstanding [Roll Forward]
Beginning Balance (in shares)			38,117,840	38,192,000
Common stock issued for employee stock plans (in shares)			452,000	719,000
Repurchase of common stock (in shares)	(46,636)	(175,000)	(657,136)	(664,945)
Ending Balance (in shares)	37,907,127	38,218,000	37,907,127	38,218,000
Shares repurchased from employees (in shares)			6,305	27,852
Cost of shares repurchased from employees			$ 1.6	$ 6.2
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)			(657,000)	(665,000)