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REPREZENTAREA NUMERELOR NATURALE PE AXA. COMPARAREA SI ORDONAREA.


REPREZENTAREA NUMERELOR NATURALE PE AXA. COMPARAREA SI ORDONAREA.




REPREZENTAREA NUMERELOR NATURALE PE AXA. COMPARAREA SI ORDONAREA .

Fie d o dreapta pe care alegem un punct O caruia ii asociem numarul 0.Literei A ii asociem numarul 1, lui B numarul 2 etc.

OA=AB=BC=CD=




Putem astfel asocia oricarui numar natural un punct pe dreapta si spunem ca am reprezentat numerele naturale pe axa numerelor.

Dreapta d se numeste suportul axei; punctul O se numeste originea axei; sensul de parcurgere a dreptei de la O spre D se numeste sensul de crestere a valorilor reprezentate pe axa. Lungimea unui singur segment OA se numeste unitate de masura. Axa numerelor se mai numeste si axa de coordonate, iar in acest caz putem spune de exemplu ca 3 reprezinta coordonata punctului C, notand C(3).

Daca se dau doua numere naturale oarecare a,b avem doar urmatoarele relatii intre ele:

1.                                                                                                                                                                                                                                                                                                                              a<b ;

2.                                                                                                                                                                                                                                                                                                                              a>b ;

3.                                                                                                                                                                                                                                                                                                                              a=b ;

Cantitatea scrisa in stanga simbolului se numeste membrul stang, iar aceea scrisa in partea dreapta se numeste membrul drept.

Proprietatile egalitatii.

1.                                                                                                                                                                                                                                                                                                                              Reflexivitatea: a=a





2.                                                                                                                                                                                                                                                                                                                              Simetria: daca: a=b si b=a

3.                                                                                                                                                                                                                                                                                                                              Tranzitivitatea: a=b si b=c atunci si a=c

Inegalitatile pot fi de doua tipuri:

- stricte sau

- nestricte sau

Inegalitatea are proprietatea de tranzitivitate:

Compararea numerelor naturale

Pentru a compara doua numere naturale cu un numar egal de cifre, se compara cifra cu cifra, incepand de la stanga, pana cand doua cifre cu acelasi ordin sunt diferite. Este mai mare numarul cu cifra respective mai mare.

Exemple.

128>127; 1285>1275; 128543>128541

Daca numerele nu au acelasi numar de cifre este mai mare numarul cu un numar mai mare de cifre.

128<12845

Exercitii

1.                                                                                                                                                                                                                                                                                                                              Determinati numerele naturale n care indeplinesc conditiile:

a)                                                                                                                                                                                                                                                                                                                              n are doua cifre si n>98




b)                                                                                                                                                                                                                                                                                                                              n are trei cifre identice si n<445

c)                                                                                                                                                                                                                                                                                                                              n este numar impar si 128<n<134

2.                                                                                                                                                                                                                                                                                                                              Ordonati crescator numerele: 436, 236, 2518, 3254, 231, 4367, 234156, 12342.

Aproximarea numerelor naturale

Cand avem un numar pe care nu trebuie sa-l exprimam cu exactitate, putem aproxima (rotunji) numarul.

Exemple.

1.                                                                                                                                                                                                                                                                                                                              Numarul 52 este mai apropiat de 50 decat de 60, deci il putem aproxima cu 50.Aproximarea se face prin lipsa.



2.                                                                                                                                                                                                                                                                                                                              Numarul 58 este mai apropiat de 60, deci il putem aproxima cu 60.Aproximarea se face prin adaos.

3.                                                                                                                                                                                                                                                                                                                              120 easte mai apropiat de 100 decat de 200, deci il putem aproxima la 100.

4.                                                                                                                                                                                                                                                                                                                              1260 il putem aproxima la 1300.

Observam ca putem aproxima in functie de ordinul de marime al unei cifre.

Exercitii.

1. Aproximati dupa ordinul de marime numerele:

a) 27, 52, 94

b) 342, 485, 682, 198

c) 4236, 2985, 9362, 3648

2. Scrieti toate numerele cuprinse intre 70 si 80 care pot fi aproximate la 70 respectiv la 80.







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