KumiswaIsayensi

Isisekelo sesistimu yezinombolo. ISIBONELO nepozitsionnyh inombolo izinhlelo

Inombolo uhlelo - kuyini? Ngisho ngaphandle kokwazi impendulo yalo mbuzo, ngamunye wethu ngempela empilweni yakho uyawuthanda numeration izinhlelo futhi akazi ngakho. Kunjalo, laba sebuningini! Lokhu akusilo elilodwa, kodwa amaningi. Ngaphambi kokunikeza izibonelo netinkhomba nepozitsionnyh, ake sibheke le nkinga, sizoxoxa izinhlelo positional, futhi.

Isidingo akhawunti

Kusukela ezikhathini zasendulo, abantu babe isidingo ukusebenzisa, okungukuthi intuitively bazi ukuthi udinga ngandlela-thile ukuveza umbono ambalwa of izinto nemicimbi. Ubuchopho ekutshela ukuthi udinga ukusebenzisa izinto ukubala. I elula kunazo bekulokhu iminwe yakhe, futhi lokhu kuyaqondakala, ngoba zihlala zitholakala (nge okumbalwa).

Lokho kwadingeka ilungu endala kanye ukuphila kohlanga lwesintu ukugoba iminwe yakhe ngomqondo ongokoqobo - isho inani mammoth efile, isibonelo. Amagama akhawunti anjalo izakhi engazange abe khona, kodwa isithombe ezibukwayo, ukuqhathanisa.

Modern positional uhlelo inombolo

Inani System - indlela (indlela yekambiso) sibe amagugu ambalwa kanye nenani izinhlamvu ezithile (izinhlamvu noma ubuningi).

Kufanele kuqondwe ukuthi onjalo nepozitsionnyh positional nomthofu ngaphambi kokunikeza izibonelo inombolo nepozitsionnyh izinhlelo. inombolo positional uhlelo setha. Manje asetshenziswa emikhakheni ehlukahlukene kanje: kanambambili (kuhlanganisa izingxenye ezinkulu ezimbili kuphela: 0 no-1) Senary (Inani lezinhlamvu - 6), octal (amadijithi - 8) duodecimal (izinhlamvu nambili), HEX (kuhlanganisa eyishumi nesithupha ubuningi). Umugqa ngamunye lezinhlamvu amasistimu iqala ngo-zero. Ubuchwepheshe banamuhla ikhompyutha esekelwe ukusetshenziswa ikhodi kanambambili - kanambambili notation positional.

Decimal uhlelo inombolo

Positional yilona khona amazinga izikhundla abalulekile, okuyinto zitholakala uphawu inombolo obuhlukahlukene. Lokhu engcono efanekiselwa idesimali inombolo system. Phela, thina zijwayele ke kusukela ebuntwaneni. Izimpawu kulesi simiso eziyishumi: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Thatha inombolo 327. Kunamadijithi ezintathu 3, 2, 7. Ngamunye wabo itholakala endaweni yayo ( indawo). Seven uthatha isikhundla yabelwe inani elilodwa (amayunithi), Deuce - inqwaba, futhi kathathu - zamakhulu. Njengoba isibalo u-enamadijithi amathathu-ke, usibeka endaweni ezintathu nje.

Ngokusekelwe kulokhu okungenhla, inombolo enamadijithi amathathu-idesimali kungenziwa bachazwa futhi ngalendlela: amathathu namashumi, kanye amayunithi amabili nesikhombisa. Futhi ukubaluleka (ukubaluleka) isikhundla yabalwa kusukela kwesokunxele kuya kwesokudla, kusuka isikhundla ababuthakathaka (iyunithi) ukuba namandla (amakhulu).

Sasizigqokele nokuzwakala ukhululekile kakhulu idesimali positional inombolo system. Thina ezandleni iminwe eziyishumi ngezinyawo zawo - kanye. Five plus emihlanu - ngakho, sibonga iminwe, thina kalula ukucabanga ebuntwaneni zamashumi. Yingakho kukhona lula ngezingane ukuba bafunde etafuleni ukubuyabuyelela amahlanu neshumi. Futhi kulula ngakho ukufunda ukubala imali yamaphepha, ngokuvamile zesi (ie ihlukaniswe ngaphandle umsalela) emihlanu futhi ngikhuthele eziyishumi.

Okunye positional uhlelo inombolo

Lamangala eziningi, kumelwe kushiwo ukuthi hhayi kuphela ingqondo yethu ojwayele ukwenza ezinye izibalo idesimali nokubala uhlelo. Kuze kube manje, abantu isebenzisa Senary futhi Duodecimal. Lokho, kulesi simiso kukhona izinhlamvu eziyisithupha kuphela (e Senary): 0, 1, 2, 3, 4, 5. Ngesikhathi nambili duodecimal yabo: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 , A, B, lapho A - yinani 10, - inombolo 11 (kusukela uphawu kufanele kube elilodwa).

Uzenzela isinqumo. Sikholelwa isikhathi Izithupha, akunjalo? Omunye ihora - ayisithupha imizuzu (amashumi ayisithupha), usuku olulodwa - kuba amahora amabili nane (izikhathi ezimbili nambili) ngonyaka - izinyanga eziyishumi nambili, nokunye ... Zonke isikhathi Slots ukulingana kalula izinombolo ezineminyaka ephakathi kuka futhi duodecimal. Kodwa thina kanjalo esetshenziswa ke, singazi ngisho ukucabanga kokufunda isikhathi.

inombolo Nonpositional uhlelo. unary

Udinga ukunquma yilokhu kuba - nepozitsionnyh uhlelo inombolo. Lena uhlelo okungokomfanekiso, lapho kungekho isikhundla ngoba inani lezinhlamvu, noma isimiso 'ukufunda' isikhundla izimele. It Ubuye siqu imithetho entry yayo futhi izibalo.

Nazi ezinye izibonelo nepozitsionnyh izinhlelo inombolo. Ase sibuyele emuva ezikhathini zasendulo. Abasebenzisi badinga i-akhawunti bese beveza kokusungulwa kakhulu elula - ngamaqhubu. inombolo Nonpositional uhlelo nodular. Omunye kuncike (isikhwama irayisi, inkunzi, inqwaba , njll) Babalwa, isibonelo, lapho uthenga noma abathengisayo ifindo eliboshwe e intambo.

Ngenxa yalokho, intambo uthola ifindo abaningi, ukuthi izikhwama eziningi irayisi uthenge (njengesibonelo). Kodwa-ke futhi kungaba notch induku lokhuni olukulesi isisekelo sawo esakhiwe ngamatshe, njll Lolu hlelo izinombolo owayemuhle wayebizwa ngokuthi lumpy. It has a igama lesibili - unary, noma eyodwa ( "uno" kusho Latin "omunye").

Kuba sobala ukuthi uhlelo inombolo - nepozitsionnyh. Phela, ngalokho izikhundla le esikhuluma ngayo lapho (isikhundla) eyodwa kuphela! Okudidayo ukuthi, kwezinye izingxenye Umhlaba namanje ngesibalo unary uhlelo vogue nepozitsionnyh.

Futhi ukuze nepozitsionnyh uhlelo inombolo zihlanganisa:

  • Roman (ngokubhala izinombolo izincwadi ezisetshenziswa - elifunyenwe);
  • Ancient (izimpawu ezifana LamaRoma, babephinde basetshenziswe) waseGibhithe;
  • zamagama (wasebenzisa izinhlamvu zamagama);
  • WaseBhabhiloni (umbhalo we-cuneiform - esetshenziswa eqondile prevernuty "nhlonhlo");
  • NgesiGreki (okubhekiselwa kuzo nangokuthi zamagama).

ISigungu esiphethe umbuso waseRoma uhlelo inani

Ancient uMbuso WaseRoma, kanye isayensi yayo, wayeyithanda intuthuko. Okuwukuphela kwesizathu esenza amaRoma wanika emhlabeni ezisunguliwe ewusizo eminingi yobuciko, kuhlanganise uhlelo akhawunti yayo. Eminyakeni engamakhulu amabili edlule, izinombolo zesiRoma abangu lisetshenziselwa ukubonisa amanani kwemibhalo ibhizinisi (kanjalo sigweme mbumbulu).

zesi-Roman - isibonelo uhlelo inombolo nonpositional, ke yaziwa kithi manje. uhlelo zaseRoma esetshenziswa ngenkuthalo, kodwa hhayi izibalo, futhi ngasinda okubhekiswe izenzo. Ngokwesibonelo, usebenzisa izinombolo zesiRoma selisho izinsuku zomlando, ekhulwini, ivolumu izinombolo, izigaba, kanye izahluko encwadini izincwadi. Ngokuvamile esetshenziselwa umhlobiso izimpawu ongumRoma dials amahora. Futhi isibonelo zesi-Roman nonpositional Isisekelo sesistimu yezinombolo.

Okuwukuphela kwesizathu esenza amaRoma esiqokiwe izinombolo izinhlamvu zesiLatini. Futhi isibalo sazo irekhodwe ngalokuhlelekile imithetho ethile. Kukhona uhla lwezinhlamvu ukhiye ohlelweni Roman inani, ngazo zalotshwa zonke izinombolo, ngaphandle kokukhetha.

Isikhundla izinombolo kohlelo Roman inani

Inombolo (e idesimali)

izinombolo Roman (incwadi-Latin)

1 mina
5 V
10 X
50 L
100 C
500 D
1000 M

Imithetho okukhiwa iinomboro

Inombolo edingekayo etholwe ngokungeza izinhlamvu (izincwadi Latin) futhi kuhlaziywa sum yabo. Cabanga indlela ngokomfanekiso izimpawu abhalwe yamaRoma, futhi kanjani kudingeka babe "funda". Sibala ngemithetho eyisisekelo yakulelo kumiswa izinombolo LamaRoma inani uhlelo nonpositional.

  1. Inombolo ezine - IV, yakhiwa izinhlamvu ezimbili (I, V - eyodwa futhi ezinhlanu). It is etholwe ngokukhipha uphawu encane ngaphezulu uma imele kwesobunxele. Lapho uphawu elincane ngakwesokudla, kubalulekile ukwengeza, bese uthola inombolo eziyisithupha - VI.
  2. Kuyadingeka ukwengeza uphawu ezimbili ezifanayo bemi eduze. Ngokwesibonelo: SS - 200 (C - 100) noma XX - 20.
  3. Uma inombolo uhlamvu lokuqala ingaphansi wesibili, wesitsatfu ochungechungeni kungaba uphawu ogama value namanje ezincane kulokuqala. Ukuze ugweme ukudideka, sikunikeza isibonelo: CDX - 410 (idesimali).
  4. Ezinye bebaningi kungenziwa amelwe ngezindlela ezahlukene, okuyinto ingenye downsides ESonto LamaRoma nokubala uhlelo. Nazi ezinye izibonelo: MVM (yamaRoma) = 1000 + (1000 - 5) = 1995 (uhlelo idesimali) noma MDVD = 1000 + 500 + (500 - 5) = 1995 Futhi akuzona zonke izindlela.

namaqhinga izibalo

inombolo Nepozitsionnyh uhlelo - lena ngezinye izikhathi isethi eziyinkimbinkimbi imithetho lezinombolo obumba, ukucutshungulwa yabo (imisebenzi kubo). imisebenzi Aritmethikhi ngesibalo nepozitsionnyh izinhlelo - akulula abantu yesimanje. Asazi umona a zezibalo laseRoma!

ISIBONELO kwalokho. Ake sizame ukungeza izinombolo ezimbili: XIX + XXVI = XXXV, lo msebenzi wenziwa ngezinyathelo ezimbili:

  1. Eyokuqala - bese uthatha ingxenye encane izinombolo tente: IX + VI = xv (mina V mina emva ngaphambi X "ngokubulala" komunye nomunye).
  2. Okwesibili - tente amasheya elikhulu nje izinombolo ezimbili: X + XX = XXX.

Ukukhupha wenziwa kancane kuyinkimbinkimbi nakakhulu. Yehlisa inani ukuhlukaniswa edingekayo ku izakhi zalo ephambili, futhi ngemva kwalokho incipha futhi ususa ukunciphisa izimpawu impinda. Of 500 Khupha 263:

D - CCLXIII = CCCCLXXXXVIIIII - CCLXIII = CCXXXVII.

Ukubuyabuyelela zesi-Roman. By the way, kubalulekile ukusho ukuthi amaRoma akazange abe nezimpawu arifmetichekih imisebenzi, bamane izwi ngabo.

Multiplicand uphindaphinde inombolo edingekayo ukuze uphawu ngamunye Okuphindaphinda, uthola izingcezu eziningana ukuthi kufanele eligoqiwe. Ngale ndlela ukukhiqiza ukuphindwaphindwa Polynomials.

Ngokuphathelene division, inqubo ohlelweni Roman inani yayiyindlela siyisinqumo esinzima kunazo zonke. Khona-ke ukusebenzisa izikolo sasendulo saseRoma - abhakhasi. Ukuze usebenze naye abantu abaqeqeshiwe (hhayi wonke umuntu wakwazi ukufunda isayensi).

On izinhlelo ukushiyeka nepozitsionnyh

Njengoba kushiwo ngenhla, zikhona nemiphumela ethile engathandeki, noma yikuphi ukuphazamiseka ngesibalo ukusetshenziswa nepozitsionnyh izinhlelo. Unary ilula ngokwanele i-akhawunti ye elula, kodwa izibalo futhi izibalo eziyinkimbinkimbi, akudingekile neze.

ERoma ayikho imithetho ezivamile for kumiswa izinombolo ezinkulu futhi kukhona lokudlela, futhi kunzima kakhulu ukwenza izibalo. Ngaphezu kwalokho, iningi inani elikhulu, okungase eyabhalwa Roma ngosizo indlela yakhe, kwaba 100,000.

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