The decimal dongosolo chiwerengero: m'munsi, zitsanzo, ndi kumasulira mu dongosolo ena ambiri

Kuyambira nthawi munthu woyamba anazindikira yokha chinthu yoyenda yokha mu dziko, ndinayang'ana pozungulira, kuswa uzingopitirira kupulumuka zosaganiza, iye anayamba kuphunzira Baibulo. Anayang'ana, poyerekeza, ndinali apeza anapanga. Ndi mu zochita zooneka ngati maziko amene tsopano ali pansi pa mphamvu ya mwanayo ndipo anayamba kumanga sayansi yamakono.

Kodi ntchito?

Choyamba tiyenera kudziwa kuti ambiri akuimira dongosolo chiwerengero. Mfundo za manambala makonzedwe umboni, chifaniziro awo zithunzi, zomwe zimatithandiza ndondomeko ya cognition. Paokha, chiwerengero kulibeko (atikhululukire Pythagoras, amene ankakhulupirira chiwerengero cha maziko a chilengedwe chonse). Izi imangokhala umboni zinthu ndi zifukwa mwakuthupi kuwerengetsera muyeso pachiyambi. Ziwerengero - zinthu kumene chiwerengero cha zigawo.

kuyambira

Choyamba atauzidwa ndi kuvala makhalidwe ambiri wosazindikira. Tsopano imatchedwa nonpositional dongosolo chiwerengero. Zochita chiwerengero kumene malo a zanyengo constituent ogwirizana. Mwachitsanzo, mipiringidzo wamba, aliyense wa Chofanana chinthu makamaka mu ofanana atatu anthu |||. Ngati kapena ayi, mipiringidzo atatu - izo ziri chimodzimodzi dashes onse atatu. Ngati inu kutenga Mwachitsanzo kwambiri, Novgorod wakale mwayi nkhani ya zilembo Asilavo. Pamene muyenera kuonetsetsa ambiri pa kalata basi kupirira ~. Komanso alifabeti dongosolo chiwerengero unachitikira wofunika kwambiri pakati pa Aroma wakale, kumene chiwerengero - Ichi ndi makalata, koma kale a ku zilembo Latin.

Chifukwa kudzipatula mphamvu wakale, omwe anayamba sayansi awo, amene wochuluka. Kumbukirani kuti njira dongosolo decimal anaikidwa kuphatikizapo Aigupto. Komabe, "wachibale" maganizo bwino kuti ife tingathe kukhala monga mfundo ya mawerengedwe anali osiyana, anthu a Egypt ntchito nambala khumi monga m'munsi, mu madigiri mawu.

kunkafunika kuunikila kukha ndi chitukuko ndi kuvuta kumvetsa ndondomeko dziko. Tiyerekeze kuti tili mwanjira kukonza kukula kwa asilikali a boma, lomwe amayezedwa zikwi (kwambiri). Chabwino tsopano wamphamvu mankhwala nkhuni? Chifukwa cha zimenezi, akatswiri Chisumeriya wa zaka apeza dongosolo nambala imene khalidwe malo chifukwa kumaliseche. Apanso, chitsanzo: manambala 789 ndi 987 chimodzimodzi "dongosolo", koma chifukwa cha kusintha manambala malo, lachiwiri ndi yokulirapo.

Kodi izo - ndi decimal dongosolo nambala? chowaloleza

Inde, malo ndi chitsanzo sanali chimodzimodzi njira zonse mawerengedwe. Mwachitsanzo, ku Babulo anachita m'munsi nambala 60, mu Greece - dongosolo alifabeti (chiwerengero cha makalata anali). N'zochititsa chidwi kuti njira kuwerenga okhala m'Babulo, ndi moyo lero - anapeza malo ake zakuthambo.

Komabe, izo zinagwira ndi kufalitsa imene radix - dazeni, wotchulidwa mosapitirira zikufanana ndi zala za manja a anthu. Weruzani nokha - alternately kupinda zala mukhoza kuziwerenga pafupifupi chitsanzo wopandamalire.

Magwero a dongosolo lino anayamba mu India, pamene iye anaonekera yomweyo pamaziko a "10". Mapangidwe nambala ya maina anali pawiri - mwachitsanzo, 18 akhoza kukalembetsa mawu ndi monga "khumi" ndipo monga "makumi awiri popanda." Ndiponso, asayansi Indian kuti anadziŵa chinthu chotero monga "ziro", yokhala olembedwa chikuoneka m'zaka IX. Iwo stepi ino wakhala ofunika mapangidwe a chakale dongosolo chiwerengero Pamalo, chifukwa ziro, ngakhale kuti likuimira wosayenera kanthu akhoza kuthandiza nambala pang'ono, kuti sanataye tanthauzo lake. Mwachitsanzo: 100000 ndipo 1. Nambala yoyamba zikuphatikizapo manambala 6, yoyamba - unit, ndi zomalizira zisanu akuimira opanda, pakalibe, ndipo nambala yachiwiri - imodzi yokha. Mwanzeru iwo ayenera kukhala wolingana, komabe si choncho. Ziro mu 100000 akusonyeza pamaso pa kukha anthu, limene nambala wachiwiri. Apa muli "kanthu".

modernity

Dongosolo chiwerengero decimal wapangidwa manambala kuyambira ziro ndi inayi. Manambala kukopedwa mkati mwake, kumadalira pa mfundo zotsatirazi:

rightmost manambala limasonyeza unit, phazi limodzi lamanzere - kupeza khumi, chinthu china lamanzere - zana, ndi zina zotero. Ndizovuta? Palibe zangati! Ndipotu decimal dongosolo zitsanzo kupereka zithunzi kwambiri, kutenga osachepera 666 Amakhala manambala atatu 6, omwe amaimira gulu. Komanso, mawonekedwe a kulemba ndi chabe. Ngati mukufuna kutsindika zimene chimodzimodzi chiwerengero mu funso, akhoza kufalitsidwa, kuperekedwa mu kulemba kuti "amamutcha" mau anu mumtima nthawi iliyonse inu mukuona angapo - "mazana asanu ndi sikisite-sikisi." kulemba Nkosafuna zikuphatikizapo onse a anthu chomwecho, makumi ndi mazana, ndiko kuti, malo a wina ndi manambala ndi kuchulukitsa ndi ena mphamvu ya nambala 10. kukodzedwa mawonekedwe ndi mawu awa:

6x10 = 666 ₁₀ ^{2 + 6 * 10 1 + 6} * 10 0 = 600 + 60 + 6 .

oloŵa panopa

The chachiwiri wotchuka pambuyo dongosolo decimal nambala wamng'ono zokwanira zosiyanasiyana - bayinare (bayinare). Zikuoneka chifukwa cha ubiquitous Leibniz, amene adakhulupirira kuti nthawi makamaka zovuta kuphunzira chiphunzitso cha nambala ya bayinare adzakhala yabwino kuposa manambala khumi. ubiquity ake, iye analandira ndi chitukuko cha luso digito, ngati iwo ali mu chiwerengero m'munsi 2 ndi nyengo ntchitoyi analemba ku kanjedza 1 ndi 2. Wolemba pulogalamu zambiri amapezeka mu dongosolo, kuyambira 1 - pamaso pa mbendera 0 - palibe. Kuchokera pa mfundo imeneyi, tingasonyeze zitsanzo zingapo fanizo kusonyeza kutengerapo dongosolo decimal.

M'kupita kwa nthawi, njira zokhudzana mapulogalamu anakhala chipangizo kwambiri, kotero anayambitsa njira ya manambala kulemba zimene kugona patsinde pa 8 ndi 16. N'chifukwa chiyani iwo? Choyamba, chiwerengero cha anthu otchulidwa kwambiri, kenako nambala kudzakudikira yankholi, ndipo kachiwiri - iwo zochokera mphamvu ya ziwiri. dongosolo Octal imakhala ya manambala 0-7, ndi hexadecimal - wa manambala chomwecho chimene decimal makalata kuphatikiza kuchokera A kuti F.

Mfundo ndi njira yomasulira

Kumasulira mu dongosolo decimal zokwanira basi kutsatira mfundo zotsatirazi: nambala oyambirira analembedwa polenomiyo, amene wapangidwa limanena katundu wa nambala aliyense pamaziko a "2" anamuukitsa kwa mlingo yoyenera pokha.

Chilinganizo zofunikira kuwerengetsa:

x2 y n'zofanana K 2 K-1 + Y K-2 K-1 2 + Y 2 K-2 K-3 + ... + Y 2 + Y 1 2 1 2 0.

Zitsanzo yomasulira

Kulimbitsa kuganizira mawu ambiri:

101111 ₂ = (1x2 ⁵⁾ + (0x2 ⁴⁾ + (1x2 ³⁾ + (1x2 ²⁾ + (1x2 ¹⁾ + (1x2 ^{0) = 32 + 8 + 4} + 2 + 1 = 47 10 .

Powonjezera pa vutolo, chifukwa dongosolo zikuphatikizapo yomasulira ndi fractional manambala, chifukwa ichi, tikambirana payokha lonse ndi fractional gawo payokha - 111,110.11 _2.:

111110.11 ₂ = (1x2 ⁵⁾ + (1x2 ⁴⁾ + (1x2 ³⁾ + (1x2 ²⁾ + (1x2 ¹⁾ + (0x2 ^{0) = 32 + 16 + 8} + 4 + 2 = 62 10 ;

November ₂ = 2 ^-1 x1 + 2 ^-2 x1 = 1/2 + 1/4 = 0,75 _10.

Chifukwa cha zimenezi, tikuona kuti ₂ = 62.75 111,110.11 _10.

Pomaliza

Ngakhale onse "masiku amakedzana", ndi decimal dongosolo chiwerengero zitsanzo zimene takambirana pamwambapa, anali akadali "pa kavalo" ndipo deduct izo kuchokera nkhanizi, si koyenera. Kuti amakhala maziko masamu mu sukulu, chitsanzo chake kudziwa malamulo maganizo masamu, amasonyeza mphamvu ya kumanga ubale umboni. Inde, kuti kwenikweni kumeneko - pafupifupi dziko lonse amagwiritsa dongosolo imeneyi, sanafooke ndi sikuthandiza ake. Chifukwa cha ichi chimodzi: ndi yabwino. Mfundo maziko mupewe iliyonse, mungathe, ngati n'koyenera, zidzakhala ngakhale apulo, koma chifukwa kusokoneza zinthu? Mwangwiro-anatsekula chiwerengero cha manambala, ngati n'koyenera, mukhoza kuziwerenga pa zala.