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Common Stock and Related Matters - Schedule of Changes in Common Stock (Details) - USD ($) shares in Millions, $ in Millions | 12 Months Ended
--- | ---
Aug. 31, 2024 | Aug. 31, 2023 | Aug. 31, 2022
Common Stock [Roll Forward] |  |  |
Balance beginning of period (in shares) | 54.4 |  |
Balance, beginning of period | $ 0.5 |  |
Stock options exercised | $ 12.0 | $ 1.2 | $ 10.7
Balance end of period (in shares) | 54.6 | 54.4 |
Balance end of period | $ 0.5 | $ 0.5 |
Common Stock |  |  |
Common Stock [Roll Forward] |  |  |
Balance beginning of period (in shares) | 54.4 | 54.2 | 54.0
Balance, beginning of period | $ 0.5 | $ 0.5 | $ 0.5
Vesting of share-based payment awards (in shares) | 0.1 | 0.2 | 0.1
Vesting of share-based payment awards | $ 0.0 | $ 0.0 | $ 0.0
Stock options exercised (in shares) | 0.1 | 0.1 | 0.1
Stock options exercised | $ 0.0 | $ 0.0 | $ 0.0
Balance end of period (in shares) | 54.6 | 54.4 | 54.2
Balance end of period | $ 0.5 | $ 0.5 | $ 0.5

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- Definition Total number of common shares of an entity that have been sold or granted to shareholders (includes common shares that were issued, repurchased and remain in the treasury). These shares represent capital invested by the firm's shareholders and owners, and may be all or only a portion of the number of shares authorized. Shares issued include shares outstanding and shares held in the treasury. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Topic 210 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SX 210.5-02(29)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1 + Details
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- Definition Aggregate par or stated value of issued nonredeemable common stock (or common stock redeemable solely at the option of the issuer). This item includes treasury stock repurchased by the entity. Note: elements for number of nonredeemable common shares, par value and other disclosure concepts are in another section within stockholders' equity. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Topic 210 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SX 210.5-02(29)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1 Reference 2: http://www.xbrl.org/2003/role/exampleRef -Topic 852 -SubTopic 10 -Name Accounting Standards Codification -Section 55 -Paragraph 10 -Publisher FASB -URI https://asc.fasb.org/1943274/2147481372/852-10-55-10 Reference 3: http://www.xbrl.org/2003/role/disclosureRef -Topic 944 -SubTopic 210 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SX 210.7-03(a)(22)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147478777/944-210-S99-1 + Details
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