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ApirmyX sMiKAWvW

ApirmyX sMiKAWvW. ivSw : ihswb jmwq : nOvIN AiDAwie : 1. srkwrI sYkMfrI skUl kilAwx suKw , biTMfw [. AiDAwpk: gurnwm isMG. poRjYkt dy audyS:- 1.b`icAW dI gixq iv`c rucI pYdw krnI[ 2.Awm jIvn iv`c gixq dI mh`qqw bwry jwxkwrI dyxw[

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ApirmyX sMiKAWvW

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  1. ApirmyX sMiKAWvW ivSw: ihswb jmwq: nOvIN AiDAwie: 1 srkwrIsYkMfrIskUlkilAwxsuKw, biTMfw [ AiDAwpk: gurnwm isMG

  2. poRjYkt dy audyS:- 1.b`icAW dI gixq iv`c rucI pYdw krnI[ 2.Awm jIvn iv`c gixq dI mh`qqw bwry jwxkwrI dyxw[ 3. rojwnw vrqoN iv`c Awaux vwly gixq bwry d`sxw[ 4.sDwrn audwhrxW dy ky ApirmyX sMiKAWvW bwry d`sxw[ 5. srl ivDI rwhIN b`icAW nMU ApirmyX sMiKAWvW bxwauxw isKwauxw[

  3. AsI jwxdy hW ik pirmyX sMiKAw auh sMiKAW hMudI hY[ • ijs nMU p/q dy rUp iv`c iliKAw jw skdw hovy, ij`Qy p Aqy q dovy sMpUrn sMiKAwvw hox Aqy q ≠ 0 hovy[

  4. pirmyX sMiKAwvw dy imAwrI rUp dw smUh • jdoN q ie`k pRwikRiqk sMiKAw hY Bwv p qy q dw AMk 1 qo isvwey koeI sWJw nw hovy[ • ie`k pirmyX sMiKAw Dn ho skdI hY jykr p Aqy q dy ieko ijhy icMn hox[

  5. ie`k pirmyX sMiKAw irx ho skdI hY jykr p Aqy q dy icMn ie`k dUjy qoN ault hox[

  6. ie~kpirmyXisPrdybrwbrhY, jyp = 0. • iesyqrW, AsINkihskdyhWikswrIAWsMpUrxsMiKAWvWnUMp/q, q≠ 0 dyrUpiv~cdrswieAwjwskdwhY, ij~Qy hr q = 1 hovy[ iesleI, sMpUrnsMiKAWvWdwsmUhpirmyXsMiKAWvWdysmUhiv~cpwieAwjWdwhY[

  7. SWq dSmlv rUp nUM ies qrW pirBwiSq kIqw jw skdw hY – pirmyX sMiKAw SWq dSmlv rUp iv~c jW ijs iv~c dSmlv rUp dI AwKrI h`d Bwg ivDI dy AMkW qy Kqm ho jWdI hY jW kuJ pgW iv`c pUrI qrW Kqm ho jWdI hY[

  8. dSmlv rUp nUM pirmyX sMiKAw dy p/q rUp iv~c bdl ky drswauxw[ • AsIN dyiKAw hY ik pirmyX sMiKAw nUM SWq jW ASWq duhrwaudy dSmlv dy rUp iv~c drswieAw jw skdw hY[ hux, AsIN ies qoN ault isKWgy, ik id`qI hoeI dSmlv aus dy pirmyX sMiKAw dy p/q rUp iv~c ikvyN drswieAw jw skdw hY[

  9. audwhrn 0.15=15 100 =15÷5 100÷5 = 3 20

  10. jdo dSmlv ASwq duhrwaudy dSmlv rUp iv~c hovy • ASwq duhrwaoudy dSmlv dy do qrHw dy dSmlv rUp hn

  11. Su~D duhrwaudy dSmlv : ie~k dSmlv ijs iv~c dSmlv qo A~gy vwly swry AMk Pyr dubwrw duhrw huMdy hn Aqy huMdy rihdy hn[ ies qrHw dy dSmlv nMU Su~D duhrwaudy dSmlv rUp kihMdy hn[

  12. audwhrn audwhrn 0.6 h~l : mMn lau x =0.6, Pyr, x=0.666……………………(1) ie~Qy swfy kol isrP ie~ko duhrwaudw AMk hY[ ies leI, AsI (1) dy dovy pwisAw nMU 10 nwl guxw krx qy prwpq krwgy[

  13. h~l 10x=6.666…………………………(2) (2) iv~co (1)nMU Gtwaux qy, swnMU pRwpq hMudy hY, 10x-x=(6.66……)-(0.66…) 

  14. h~l 9x=6 X=6/9 X=2/3 ies leI, 0.6=2/3

  15. ipCly BwgW iv~c AsIN dyiKAw hY ik hryk pirmyX sMiKAw jW qW SWq dSmlv rUp jW iPr ASWq duhrwauNdy hoey dSmlv rUp iv~c drsweI jw skdI hY[

  16. ijs qrW aupr d~isAw igAw hY ausqoN koeI vI sMiKAw hyT ilKy dSmlv rUpW iv~c iksy ie~k rUp iv~c drsweI jw skdI hY[ • SWq • ASWq duhrwauNdI • ASWq nw duhrwauNdI

  17. ApirmyX sMiKAw • ie~k sMiKAw ApirmyX sMiKAw khwauNdI hY jy ies dw ASWq nw duhrwauNdw hoieAw dSmlv rUp hovy[

  18. ApirmyX sMiKAw dy kuJ mhq~vpUrx q~Q • iek irxwqmk ApirmyX sMiKAw vI ApirmyX sMiKAw hI huMdI hY[ • iek pirmyX sMiKAw Aqy ApirmyX sMiKAw dw joV Aqy Gtwau vI hmySW ApirmyX sMiKAw huMdw hY[

  19. ApirmyX sMiKAw dy kuJ mhq~vpUrx q~Q • iek pirmyX sMiKAw Aqy iek ApirmyX sMiKAw dw guxnPl Aqy BwgPl vI ApirmyX sMiKAw huMdI hY[ • do ApirmyX sMiKAwvW dw joV Gtwau guxnPl jW BwgPl koeI jrUrI nhIN ik ieh vI ApirmyX hI hovy[

  20. AiBAws

  21. AiBAws 1. hyT ilKIAW pirmyX sMiKAvW nUM dSmlv rUp iv`c ilKo: • 28/100 • 227/500 • 16/5 • 2/25

  22. 2. hyT ilKIAW pirmyX sMiKAvW nUM dSmlv rUp iv`c ilKo: • 17/10 • 33/50 • 66/6 • 4/88

  23. 3.hyT ilKy dSmlv rUpW nUM p/q rUp iv~c ilKo: 0.29 2.15 6.010 8.90

  24. 4.hyT ilKy dSmlv rUpW nUM p/q rUp iv~c ilKo: 0.17 2.18 5.017 7.80

  25. Bibliography • pMjwb rwj is~iKAw borf dI ihswb ivSy dI nONvI jmwq dI pwT pusqk[ • http://www.progarchives.com/album.asp?id=10755 • http://sunbeltblog.blogspot.com/2007/07/she-loves-irrational-numbers-so-much.html • http://schools.woboe.org/teachlearn/webquests/realnumbersystem/Pages/default.aspx

  26. DMnvwd

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