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Income Taxes (Narrative) (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Feb. 28, 2023
Feb. 28, 2022
Feb. 28, 2023
Feb. 28, 2022
Income Taxes [Abstract]        
Provision for income taxes 20.80% 20.10% 20.90% 19.90%
Tax shortfalls (benefit) related to settlements of stock-based equity awards     $ 0.7 $ (0.2)
Unfavorable impact on effective tax rate due to tax shortfall     2.40%  
Favorable impact on effective tax rate due to charitable donation     1.90%  
Charitable donation amount     $ 3.5  
Tax benefit related to charitable donation     $ 0.7