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Business Acquisitions (Details) (USD $) | 12 Months Ended | 4 Months Ended
--- | --- | ---
Dec. 31, 2014 Business | Dec. 31, 2013 Business | Dec. 31, 2012 Business | Dec. 31, 2012
Business Acquisition [Line Items] |  |  |  |
Number of business acquired | 3 us-gaap_NumberOfBusinessesAcquired | 2 us-gaap_NumberOfBusinessesAcquired | 6 us-gaap_NumberOfBusinessesAcquired |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Intangible Assets Other than Goodwill |  | $ 493,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill |  |
Goodwill | 4,710,691,000 us-gaap_Goodwill | 4,549,998,000 us-gaap_Goodwill | 3,868,857,000 us-gaap_Goodwill | 3,868,857,000 us-gaap_Goodwill
Intangibles acquired |  | 493,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill |  |
Finite lived intangible assets |  | 465,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles |  |
Weighted average useful life |  | 19 years |  |
Cost of acquired entity transaction costs |  | 3,300,000 us-gaap_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts |  |
Trade Names [Member] |  |  |  |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Indefinite lived intangible assets |  | 28,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_TradeNamesMember |  |
Customer Relationships [Member] |  |  |  |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Finite lived intangible assets |  | 451,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_CustomerRelationshipsMember |  |
Weighted average useful life |  | 20 years |  |
Technology [Member] |  |  |  |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Finite lived intangible assets |  | 12,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_PatentedTechnologyMember |  |
Weighted average useful life |  | 7 years |  |
Noncompete Agreements [Member] |  |  |  |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Finite lived intangible assets |  | 2,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_NoncompeteAgreementsMember |  |
Weighted average useful life |  | 5 years |  |
Immaterial Acquisitions [Member] |  |  |  |
Business Acquisition [Line Items] |  |  |  |
Number of business acquired |  |  | 5 us-gaap_NumberOfBusinessesAcquired / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember |
Cost of acquired entity purchase price | 303,000,000 us-gaap_BusinessCombinationConsiderationTransferred1 / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember |  | 62,000,000 us-gaap_BusinessCombinationConsiderationTransferred1 / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Intangible Assets Other than Goodwill | 99,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember |  | 43,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember | 43,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
Goodwill | 208,000,000 us-gaap_Goodwill / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember |  | 16,000,000 us-gaap_Goodwill / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember | 16,000,000 us-gaap_Goodwill / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
Indefinite lived intangible assets | 7,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember |  |  |
Intangibles acquired | 99,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember |  | 43,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember | 43,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
Finite lived intangible assets | 92,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember |  | 42,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember | 42,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
Weighted average useful life | 17 years |  | 7 years |
Cost of acquired entity transaction costs | 2,800,000 us-gaap_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember |  | 1,000,000 us-gaap_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember | 1,000,000 us-gaap_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
Immaterial Acquisitions [Member] | Trade Names [Member] |  |  |  |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Indefinite lived intangible assets |  |  | 1,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_TradeNamesMember | 1,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_TradeNamesMember
Immaterial Acquisitions [Member] | Backlog [Member] |  |  |  |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Finite lived intangible assets | 1,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = rop_BacklogMember |  |  |
Weighted average useful life | 1 year |  |  |
Immaterial Acquisitions [Member] | Customer Relationships [Member] |  |  |  |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Finite lived intangible assets | 82,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_CustomerRelationshipsMember |  | 17,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_CustomerRelationshipsMember | 17,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_CustomerRelationshipsMember
Weighted average useful life | 19 years |  | 7 years |
Immaterial Acquisitions [Member] | Technology [Member] |  |  |  |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Finite lived intangible assets | 7,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_PatentedTechnologyMember |  |  |
Weighted average useful life | 6 years |  |  |
Immaterial Acquisitions [Member] | Software [Member] |  |  |  |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Finite lived intangible assets | 2,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_ComputerSoftwareIntangibleAssetMember |  |  |
Weighted average useful life | 4 years |  |  |
Immaterial Acquisitions [Member] | Unpatented Technology [Member] |  |  |  |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Finite lived intangible assets |  |  | 8,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_UnpatentedTechnologyMember | 8,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_UnpatentedTechnologyMember
Weighted average useful life |  |  | 8 years |
Immaterial Acquisitions [Member] | Patents and other protective rights Memeber |  |  |  |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Finite lived intangible assets |  |  | 16,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_PatentsMember | 16,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_PatentsMember
Weighted average useful life |  |  | 7 years |
Advanced Sensors, Ltd [Member] |  |  |  |
Business Acquisition [Line Items] |  |  |  |
Cost of acquired entity purchase price |  | 54,000,000 us-gaap_BusinessCombinationConsiderationTransferred1 / us-gaap_BusinessAcquisitionAxis = rop_AdvancedSensorsLtdMember |  |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Goodwill |  | 28,000,000 us-gaap_Goodwill / us-gaap_BusinessAcquisitionAxis = rop_AdvancedSensorsLtdMember |  |
Indefinite lived intangible assets |  | 28,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets / us-gaap_BusinessAcquisitionAxis = rop_AdvancedSensorsLtdMember |  |
Managed Health Care Associates, Inc [Member] |  |  |  |
Business Acquisition [Line Items] |  |  |  |
Cost of acquired entity purchase price |  | 1,000,000,000 us-gaap_BusinessCombinationConsiderationTransferred1 / us-gaap_BusinessAcquisitionAxis = rop_ManagedHealthCareAssociatesIncMember |  |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Current assets |  | 59,813,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssets / us-gaap_BusinessAcquisitionAxis = rop_ManagedHealthCareAssociatesIncMember |  |
Intangible Assets Other than Goodwill |  | 465,500,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill / us-gaap_BusinessAcquisitionAxis = rop_ManagedHealthCareAssociatesIncMember |  |
Goodwill |  | 678,183,000 us-gaap_Goodwill / us-gaap_BusinessAcquisitionAxis = rop_ManagedHealthCareAssociatesIncMember |  |
Other assets |  | 5,798,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets / us-gaap_BusinessAcquisitionAxis = rop_ManagedHealthCareAssociatesIncMember |  |
Total assets acquired |  | 1,209,294,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets / us-gaap_BusinessAcquisitionAxis = rop_ManagedHealthCareAssociatesIncMember |  |
Current liabilities |  | (24,717,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilities / us-gaap_BusinessAcquisitionAxis = rop_ManagedHealthCareAssociatesIncMember |  |
Long-term deferred tax liability |  | (162,503,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredTaxLiabilitiesNoncurrent / us-gaap_BusinessAcquisitionAxis = rop_ManagedHealthCareAssociatesIncMember |  |
Other liabilities |  | (6,524,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesOther / us-gaap_BusinessAcquisitionAxis = rop_ManagedHealthCareAssociatesIncMember |  |
Net assets acquired |  | 1,015,550,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet / us-gaap_BusinessAcquisitionAxis = rop_ManagedHealthCareAssociatesIncMember |  |
Fair value adjustment for admin fees related to customer purchases |  | 35,000,000 us-gaap_AssetsFairValueAdjustment / us-gaap_BusinessAcquisitionAxis = rop_ManagedHealthCareAssociatesIncMember |  |
Fair value liability related revenue-share obligation |  | 8,600,000 us-gaap_LiabilitiesFairValueAdjustment / us-gaap_BusinessAcquisitionAxis = rop_ManagedHealthCareAssociatesIncMember |  |
Intangibles acquired |  | 465,500,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill / us-gaap_BusinessAcquisitionAxis = rop_ManagedHealthCareAssociatesIncMember |  |
Sunquest Information Systems, Inc [Member] |  |  |  |
Business Acquisition [Line Items] |  |  |  |
Cost of acquired entity purchase price |  |  | 1,400,000,000 us-gaap_BusinessCombinationConsiderationTransferred1 / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Current assets |  |  | 96,883,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssets / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember | 96,883,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssets / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember
Intangible Assets Other than Goodwill |  |  | 669,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember | 669,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember
Goodwill |  |  | 993,780,000 us-gaap_Goodwill / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember | 993,780,000 us-gaap_Goodwill / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember
Other assets |  |  | 2,694,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember | 2,694,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember
Total assets acquired |  |  | 1,762,357,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember | 1,762,357,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember
Deferred revenue |  |  | (83,065,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesDeferredRevenue / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember | (83,065,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesDeferredRevenue / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember
Other current liabilities |  |  | (18,762,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesOther / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember | (18,762,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesOther / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember
Long-term deferred tax liability |  |  | (244,550,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredTaxLiabilitiesNoncurrent / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember | (244,550,000)us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredTaxLiabilitiesNoncurrent / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember
Net assets acquired |  |  | 1,415,980,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember | 1,415,980,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember
Intangibles acquired |  |  | 669,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember | 669,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember
Finite lived intangible assets |  |  | 571,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember | 571,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember
Weighted average useful life |  |  | 18 years |
Cost of acquired entity transaction costs |  |  | 6,700,000 us-gaap_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember | 6,700,000 us-gaap_BusinessAcquisitionCostOfAcquiredEntityTransactionCosts / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember
Pro Forma Sales |  |  | 3,130,407 us-gaap_BusinessAcquisitionsProFormaRevenue / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember | 69,400,000 us-gaap_BusinessAcquisitionsProFormaRevenue / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember
Pro forma Net income |  |  | 521,141 us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember | 8,800,000 us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember
Pro Forma Earnings per share, basic (in dollars per share) |  |  | $ 5.33 us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember |
Pro Forma Earnings per share, diluted (in dollars per share) |  |  | $ 5.23 us-gaap_BusinessAcquisitionProFormaEarningsPerShareDiluted / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember |
Pro Forma Earnings Adjustment for non-recurring acquisition and other costs |  |  | 50,700,000 rop_BusinessAcquisitionProFormaEarningsAdjustmentForNonRecurringAcquisitionAndOtherCosts / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember |
Sunquest Information Systems, Inc [Member] | Trade Names [Member] |  |  |  |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Indefinite lived intangible assets |  |  | 98,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_TradeNamesMember | 98,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIndefiniteLivedIntangibleAssets / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_TradeNamesMember
Sunquest Information Systems, Inc [Member] | Customer Relationships [Member] |  |  |  |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Finite lived intangible assets |  |  | 460,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_CustomerRelationshipsMember | 460,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_CustomerRelationshipsMember
Weighted average useful life |  |  | 20 years |
Sunquest Information Systems, Inc [Member] | Software [Member] |  |  |  |
Fair value of assets acquired and liabilities assumed [Abstract] |  |  |  |
Finite lived intangible assets |  |  | $ 111,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_ComputerSoftwareIntangibleAssetMember | $ 111,000,000 us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles / us-gaap_BusinessAcquisitionAxis = rop_SunquestInformationSystemsIncMember / us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis = us-gaap_ComputerSoftwareIntangibleAssetMember
Weighted average useful life |  |  | 12 years |

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