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reglas para cálculos aproximados y redondeo de números

reglas para cálculos aproximados y redondeo de números

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873 /DERUDWRULR GH 5HVLVWHQFLD GH PDWHULDOHV ± *XtD GH /DERUDWRULR<br />

(ODERUDGD SRU *DEULHO &DOOH 7UXMLOOR<br />

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/RV YDORUHV QXPpULFRV REWHQLGRV FRPR UHVXOWDGR GH PHGLFLRQHV GH PDJQLWXGHV ItVLFDV \ ORV<br />

FiOFXORV UHDOL]DGRV HQ ODV HMHFXFLRQHV GH ORV WUDEDMRV GH ODERUDWRULR VRQ DSUR[LPDGRV 6LQ<br />

HPEDUJR FRP~QPHQWH FXDQGR ORV HVWXGLDQWHV XVDQ FDOFXODGRUDV HOHFWUyQLFDV SDUD ORV<br />

FiOFXORV WLHQGHQ D SUHVHQWDU HO UHVXOWDGR ILQDO FRQ XQ JUDQ Q~PHUR GH GHFLPDOHV HV GHFLU<br />

FRQ XQD SUHFLVLyQ TXH QR HVWi JDUDQWL]DGD SRU ORV GDWRV LQLFLDOHV<br />

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SUHFLVD TXH ORV VXSXHVWRV VREUH OD TXH VH IXQGD (V SRU HVWR TXH HQ OD HMHFXFLyQ GH FiOFXORV<br />

HV QHFHVDULR UHVSHWDU XQDV UHJODV GH UHGRQGHR \ GH FiOFXORV DSUR[LPDGRV<br />

/D 7HRUtD GH ORV FiOFXORV DSUR[LPDGRV SHUPLWH<br />

&RQRFLHQGR OD SUHFLVLyQ GH ORV GDWRV LQLFLDOHV YDORUDU OD SUHFLVLyQ GHO UHVXOWDGR GH<br />

ORV FiOFXORV UHDOL]DGRV<br />

7RPDU ORV GDWRV LQLFLDOHV FRQ XQD SUHFLVLyQ WDO TXH VH JDUDQWLFH OD SUHFLVLyQ<br />

HVSHUDGD GH ORV UHVXOWDGRV<br />

/LEHUDU HO SURFHVR GH FiOFXOR GH RSHUDFLRQHV LQQHFHVDULDV ODV FXDOHV QR WLHQHQ<br />

HIHFWR HQ OD SUHFLVLyQ GHO UHVXOWDGR<br />

/D QRUPD WpFQLFD FRORPELDQD 17& -,6 = HQXQFLD ODV VLJXLHQWHV UHJODV SDUD HO<br />

UHGRQGHR GH YDORUHV QXPpULFRV<br />

&XDQGR VH UHGRQGHD XQ YDORU QXPpULFR D Q FLIUDV VLJQLILFDWLYDV R D Q OXJDUHV GHFLPDOHV<br />

ODV FLIUDV TXH HVWiQ PiV DOOi GHO GtJLWR Q pVLPR VH FRQVLGHUDUiQ DVt<br />

1RWD (O Q~PHUR GH FLIUDV VLJQLILFDWLYDV VH FRQWDUi GHVGH HO OXJDU GH OD SULPHUD FLIUD GLIHUHQWH D FHUR<br />

6L HO YDORU QXPpULFR PiV DOOi GHO GtJLWR Q pVLPR HV PHQRU TXH PHGLD XQLGDG GHO<br />

GtJLWR Q pVLPR VH GHEHUi EDMDU<br />

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GtJLWR Q pVLPR pVWH VH LQFUHPHQWDUi HQ OD XQLGDG<br />

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PLWDG GH OD XQLGDG GHO GtJLWR Q pVLPR R QR VH VDEH VL VH KD UHGRQGHDGR KDFLD DUULED<br />

R KDFLD DEDMR VH GHEHUi VHJXLU OR HVWDEOHFLGR HQ D y E<br />

D 6L HO GtJLWR Q pVLPR HV X VH UHGRQGHDUi KDFLD DEDMR<br />

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6L VH FRQRFH TXH HO YDORU QXPpULFR PiV DOOi GHO GtJLWR Q pVLPR KD VLGR UHGRQGHDGR<br />

KDFLD DUULED R KDFLD DEDMR VH GHEHUi VHJXLU HO PpWRGR y


873 /DERUDWRULR GH 5HVLVWHQFLD GH PDWHULDOHV ± *XtD GH /DERUDWRULR<br />

(ODERUDGD SRU *DEULHO &DOOH 7UXMLOOR<br />

2EVHUYDFLyQ HVWH SURFHGLPLHQWR GH UHGRQGHR VH GHEHUi KDFHU HQ XQ SDVR 3RU HMHPSOR VL<br />

VH UHGRQGHD SRU HVWH PpWRGR D FLIUDV VLJQLILFDWLYDV VH FRQYLHUWH HQ 1R VH GHEH<br />

KDFHU HQ GRV SDVRV FRPR VH PXHVWUD HQVHJXLGD<br />

SULPHU SDVR VHJXQGR<br />

+DVWD DTXt ODV UHJODV TXH RUGHQD HO HVWiQGDU 17& -,6 = VL D XVWHG OH SDUHFHQ<br />

XQ SRFR FRQIXVDV SXHGHQ XVDUVH ODV VLJXLHQWHV UHJODV XVDGDV HQ OD OLWHUDWXUD FLHQWtILFD<br />

WUDGLFLRQDO FRP~Q<br />

3DUD HO UHGRQGHR GH Q~PHURV VH GHEHQ VHJXLU ODV VLJXLHQWHV UHJODV > @<br />

(MHPSORV<br />

6L OD SULPHUD FLIUD TXH VH RPLWH DUURMD HV y HQWRQFHV OD ~OWLPD FLIUD TXH<br />

VH FRQVHUYD HQ HO Q~PHUR DSUR[LPDGR VH FRQVHUYD VLQ QLQJ~Q FDPELR UHGRQGHR FRQ<br />

GHIHFWR<br />

6L GHVSXpV GH OD ~OWLPD FLIUD FRQVHUYDGD VLJXH XQ y OXHJR GH OD FXDO<br />

VLJXH XQD R YDULDV FLIUDV VLJQLILFDWLYDV HQWRQFHV HQ QHFHVDULR VXPDU XQD XQLGDG D OD<br />

FLIUD TXH VH FRQVHUYD VL OD ~OWLPD FLIUD TXH VH FRQVHUYD HV pVWD GHEH FDPELDUVH D<br />

\ VH DXPHQWD HQ XQD XQLGDG HO YDORU GH OD SHQ~OWLPD FLIUD UHGRQGHR FRQ H[FHVR<br />

6L OXHJR GH OD ~OWLPD FLIUD FRQVHUYDGD VH WLHQH VyOR OD FLIUD y OD FLIUD VHJXLGD GH<br />

FHURV VH WRPD FRPR ~OWLPD FLIUD HO Q~PHUR SDU PiV SUy[LPR HV GHFLU VL OD FLIUD<br />

UHWHQLGD HV SDU VH GHMD \ VL HV LPSDU VH WRPD OD FLIUD VXSHULRU<br />

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DXPHQWD HQ XQD XQLGDG REWHQLpQGRVH HO Q~PHUR UHGRQGHDGR<br />

x 5HGRQGHDU HO Q~PHUR KDVWD WUHV FLIUDV VLJQLILFDWLYDV<br />

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\ HO Q~PHUR UHGRQGHDGR VHUi<br />

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3RU HMHPSOR HO Q~PHUR UHGRQGHDGR KDVWD WUHV FLIUDV VLJQLILFDWLYDV GHEH VHU<br />

UHSUHVHQWDGR FRPR ˜ y ˜ y ˜ (VWD ~OWLPD QRWDFLyQ HV OD SUHIHULGD


873 /DERUDWRULR GH 5HVLVWHQFLD GH PDWHULDOHV ± *XtD GH /DERUDWRULR<br />

(ODERUDGD SRU *DEULHO &DOOH 7UXMLOOR<br />

6L SRU HMHPSOR HO Q~PHUR WLHQH VyOR ODV GRV SULPHUDV FLIUDV FRQILDEOHV VH GHEH<br />

HVFULELU ˜<br />

(Q HO Q~PHUR KD\ FXDWUR FLIUDV FRQILDEOHV HQ HO Q~PHUR ˜ KD\ VyOR GRV FLIUDV<br />

FRQILDEOHV<br />

&XDQGR VH UHDOL]D XQ UHGRQGHR HO YDORU DSUR[LPDGR SXHGH VHU PD\RU R PHQRU TXH HO<br />

Q~PHUR H[DFWR<br />

(Q OD SUiFWLFD HQ OD PD\RUtD GH ORV FDVRV QR VH FRQRFH HO YDORU H[DFWR GHO Q~PHUR<br />

DSUR[LPDGR \ HO HUURU GH VX UHGRQGHR 6LQ HPEDUJR VLHPSUH HV SRVLEOH LQGLFDU OD PDJQLWXG<br />

GHO HUURU OtPLWH DEVROXWR 'D HO FXDO UHSUHVHQWD XQ Q~PHUR SRVLWLYR SDUD HO FXDO VH FXPSOH<br />

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VX REWHQFLyQ VH WRPD VLHPSUH LJXDO D PHGLD XQLGDG GHO RUGHQ GH OD ~OWLPD FLIUD FRQVHUYDGD<br />

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GRQGH U ± HV HO Q~PHUR GH SRVLFLRQHV GHVSXpV GH OD FRPD<br />

(MHPSOR (O Q~PHUR D WLHQH XQ HUURU OtPLWH DEVROXWR<br />

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RUGHQ GH OD ~OWLPD FLIUD<br />

/RV Q~PHURV DSUR[LPDGRV SRU OR FRP~Q VH FDUDFWHUL]DQ SRU OD FDQWLGDG GH SRVLFLRQHV<br />

GHVSXpV GH OD FRPD FRQVHUYDGDV R SRU OD FDQWLGDG GH FLIUDV VLJQLILFDWLYDV 6H OODPDQ FLIUDV


873 /DERUDWRULR GH 5HVLVWHQFLD GH PDWHULDOHV ± *XtD GH /DERUDWRULR<br />

(ODERUDGD SRU *DEULHO &DOOH 7UXMLOOR<br />

VLJQLILFDWLYDV D WRGRV ORV Q~PHURV H[FHSWR ORV FHURV D OD L]TXLHUGD (O FHUR VH FRQVLGHUD<br />

FLIUD VLJQLILFDWLYD VyOR FXDQGR HVWi HQWUH RWUDV FLIUDV VLJQLILFDWLYDV R FXDQGR HVWi DO ILQDO GH<br />

XQ Q~PHUR \ QR VH VDEH VL VH WLHQHQ XQLGDGHV GHO RUGHQ FRUUHVSRQGLHQWH HQ HO Q~PHUR GDGR<br />

(MHPSOR /RV Q~PHURV WLHQHQ WUHV FLIUDV VLJQLILFDWLYDV<br />

/DV FLIUDV HQ XQ Q~PHUR DSUR[LPDGR VRQ OODPDGDV FRQILDEOHV VL OD GLIHUHQFLD HQWUH HO<br />

Q~PHUR H[DFWR ] \ VX YDORU DSUR[LPDGR D QR HV PD\RU TXH OD PLWDG GH OD XQLGDG GHO RUGHQ<br />

GH OD ~OWLPD FLIUD GHO Q~PHUR DSUR[LPDGR TXH HQ HVWH FDVR HV HO HUURU OtPLWH DEVROXWR 'D<br />

'H PDQHUD TXH GH DFXHUGR D HVWD UHJOD WRGDV ODV FLIUDV VLJQLILFDWLYDV GH XQ Q~PHUR<br />

DSUR[LPDGR VRQ FRQILDEOHV<br />

(O HUURU GHO UHVXOWDGR GH FXDOTXLHU RSHUDFLyQ DULWPpWLFD UHDOL]DGD FRQ Q~PHURV DSUR[LPDGRV<br />

VH H[SUHVD D WUDYpV GHO HUURU GH ORV GDWRV LQLFLDOHV VREUH OD EDVH GH OD 7HRUtD GHO FiOFXOR GH<br />

HUURUHV GH IXQFLRQHV<br />

&XDQGR VH UHDOL]D XQD JUDQ FDQWLGDG GH FiOFXORV \ QR VH WLHQHQ HQ FXHQWD ORV HUURUHV GH FDGD<br />

UHVXOWDGR SRU VHSDUDGR HV QHFHVDULR UHJLUVH SRU ODV VLJXLHQWHV UHJODV ODV FXDOHV JDUDQWL]DQ<br />

OD REWHQFLyQ GH UHVXOWDGRV FRQ WRGDV ODV FLIUDV FRQILDEOHV<br />

&XDQGR VH VXPDQ \ UHVWDQ Q~PHURV DSUR[LPDGRV HV QHFHVDULR UHGRQGHDU HO UHVXOWDGR<br />

ILQDO KDVWD HO Q~PHUR PiV SHTXHxR GH FLIUDV GHFLPDOHV TXH WHQtDQ ORV GDWRV LQLFLDOHV /RV<br />

Q~PHURV TXH WLHQHQ PiV FLIUDV GHFLPDOHV HV QHFHVDULR UHGRQGHDUORV SUHYLDPHQWH<br />

FRQVHUYDQGR XQD FLIUD GHFLPDO PiV TXH ODV TXH SRVHH HO Q~PHUR FRQ PHQRV FDQWLGDG GH<br />

FLIUDV GHFLPDOHV<br />

(MHPSOR (QFRQWUDU OD VXPD<br />


873 /DERUDWRULR GH 5HVLVWHQFLD GH PDWHULDOHV ± *XtD GH /DERUDWRULR<br />

(ODERUDGD SRU *DEULHO &DOOH 7UXMLOOR<br />

&XDQGR VH HOHYD DO FXDGUDGR R DO FXER HQ HO UHVXOWDGR ILQDO VH GHEHQ FRQVHUYDU WDQWDV<br />

FLIUDV GHFLPDOHV FXDQWDV WLHQH HO Q~PHUR DSUR[LPDGR D HOHYDUVH D OD SRWHQFLD GDGD<br />

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GHFLPDOHV FXDQWDV WHQtD HO Q~PHUR EDMR HO VLJQR GH UDGLFDO<br />

(MHPSOR ([WUDHU OD UDt] FXDGUDGD GH ˜<br />

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UHVXOWDGRV LQWHUPHGLRV VH GHEH FRQVHUYDU XQD FLIUD VLJQLILFDWLYD PiV OD FXDO HQ HO UHVXOWDGR<br />

ILQDO VH DUURMD GH DFXHUGR D ODV UHJODV GH UHGRQGHR<br />

(MHPSOR (QFRQWUDU HO YDORU QXPpULFR GH OD H[SUHVLyQ<br />

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