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Income Taxes - Schedule of Change in Unrecognized Income Tax Benefit (Details) - USD ($) $ in Millions | 12 Months Ended
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Aug. 31, 2022 | Aug. 31, 2021 | Aug. 31, 2020
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward] |  |  |
Unrecognized tax benefits balance at beginning of year | $ 17.7 | $ 17.2 | $ 16.6
Additions based on tax positions related to the current year | 3.5 | 5.2 | 2.3
Additions for tax positions of prior years | 0.1 | 0.1 | 0.0
Reductions for tax positions of prior years | (0.2) | (0.1) | (0.4)
Reductions due to settlements | 0.0 | (4.6) | (1.2)
Reductions due to lapse of statute of limitations | (1.6) | (0.1) | (0.1)
Unrecognized tax benefits balance at end of year | $ 19.5 | $ 17.7 | $ 17.2

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- Definition Amount of unrecognized tax benefits. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 45 -Paragraph 10B -URI https://asc.fasb.org/extlink&oid=123427490&loc=SL37586934-109318 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 15A -Subparagraph (a) -URI https://asc.fasb.org/extlink&oid=121826272&loc=SL6600010-109319 + Details
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- Definition Amount of decrease in unrecognized tax benefits resulting from tax positions taken in prior period tax returns. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 15A -Subparagraph (a)(1) -URI https://asc.fasb.org/extlink&oid=121826272&loc=SL6600010-109319 + Details
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- Definition Amount of decrease in unrecognized tax benefits resulting from settlements with taxing authorities. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 15A -Subparagraph (a)(3) -URI https://asc.fasb.org/extlink&oid=121826272&loc=SL6600010-109319 + Details
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- Definition Amount of increase in unrecognized tax benefits resulting from tax positions that have been or will be taken in current period tax return. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 15A -Subparagraph (a)(2) -URI https://asc.fasb.org/extlink&oid=121826272&loc=SL6600010-109319 + Details
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- Definition Amount of decrease in unrecognized tax benefits resulting from lapses of applicable statutes of limitations. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 740 -SubTopic 10 -Section 50 -Paragraph 15A -Subparagraph (a)(4) -URI https://asc.fasb.org/extlink&oid=121826272&loc=SL6600010-109319 + Details
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