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Stock-based Compensation (Narrative) (Details) - USD ($) | 12 Months Ended
--- | ---
Aug. 31, 2019 | Aug. 31, 2018 | Aug. 31, 2017
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Number of shares authorized under stock plan | 1,000,000 |  |
Number of shares available for grant | 720,373 |  |
Allocated share-based compensation expense | $ 4,400,000 | $ 4,200,000 | $ 4,100,000
Employee service share-based, Tax benefit from compensation expense | $ 1,000,000.0 | 1,100,000 | 1,400,000
Stock Options [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Employee service share-based, Tax benefit from compensation expense |  | 100,000 | 400,000
Total intrinsic value of stock options exercised |  | 500,000 | 1,600,000
Restricted Stock Units [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Vesting period | 3 years |  |
Employee service share-based, Tax benefit from compensation expense | $ 1,400,000 | $ 700,000 | $ 1,300,000
Compensation cost not yet recognized | $ 600,000 |  |
Remaining weighted-average vesting periods | 1 year 7 months 6 days |  |
Weighted-average grant date fair value | $ 163.93 | $ 111.71 | $ 109.23
Total intrinsic value of stock-based awards converted into common shares | $ 6,000,000.0 | $ 2,800,000 | $ 3,600,000
Market Share Units [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Vesting period | 3 years |  |
Employee service share-based, Tax benefit from compensation expense | $ 900,000 | $ 800,000 | $ 900,000
Compensation cost not yet recognized | $ 2,100,000 |  |
Remaining weighted-average vesting periods | 1 year 10 months 24 days |  |
Weighted-average grant date fair value | $ 177.82 | $ 101.93 | $ 90.91
Total intrinsic value of stock-based awards converted into common shares | $ 4,000,000.0 | $ 3,000,000.0 | $ 2,800,000
Expected volatility period | 2 years 10 months 24 days | 2 years 10 months 20 days | 2 years 10 months 20 days
Deferred Performance Units [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Vesting period | 1 year |  |
Compensation cost not yet recognized | $ 0 |  |
Weighted-average grant date fair value | $ 160.37 | $ 110.65 | $ 110.19
Minimum [Member] | Market Share Units [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Percent of original target number of vested shares | 0.00% |  |
Minimum [Member] | Deferred Performance Units [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Percent of original target number of vested shares | 0.00% |  |
Maximum [Member] | Market Share Units [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Percent of original target number of vested shares | 200.00% |  |
Maximum [Member] | Deferred Performance Units [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |
Percent of original target number of vested shares | 100.00% |  |

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- Definition Weighted-average period over which cost not yet recognized is expected to be recognized for award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (i) -URI http://asc.fasb.org/extlink&oid=116856206&loc=d3e5070-113901 + Details
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- Definition Period over which grantee's right to exercise award under share-based payment arrangement is no longer contingent on satisfaction of service or performance condition, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. Includes, but is not limited to, combination of market, performance or service condition. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (a)(1) -URI http://asc.fasb.org/extlink&oid=116856206&loc=d3e5070-113901 + Details
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- Definition Fair value of share-based awards for which the grantee gained the right by satisfying service and performance requirements, to receive or retain shares or units, other instruments, or cash. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (d)(2) -URI http://asc.fasb.org/extlink&oid=116856206&loc=d3e5070-113901 + Details
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- Definition The difference between the maximum number of shares (or other type of equity) authorized for issuance under the plan (including the effects of amendments and adjustments), and the sum of: 1) the number of shares (or other type of equity) already issued upon exercise of options or other equity-based awards under the plan; and 2) shares (or other type of equity) reserved for issuance on granting of outstanding awards, net of cancellations and forfeitures, if applicable. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -URI http://asc.fasb.org/extlink&oid=116856206&loc=d3e5070-113901 + Details
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