Question

Determinati cifrele a,b astfel incat forma zecimala a numarul rational 1 supra 1ab(cu bara in cap) are un nr finit de zecimale

Answer 1

   
[tex]\displaystyle\\ \text{Avem fractia:}~~ \frac{1}{~~\overline{1ab}~~}\\\\ \text{Pentru ca forma zecimala a unei fractii sa aiba numar finit de zecimale,}\\ \text{trebuie ca numitorul fractiei sa aiba divizori doar 2 si/sau 5.}\\\\ \text{Rezulta ca } ~\overline{1ab} ~~\text{poate fi: }\\\\ \overline{1ab} =100=2^2\times5^2,~~a=0,~b=0\\\\ \overline{1ab}=125=5^3,~~a=2,~b=5\\\\ \overline{1ab}=128=2^7,~~a=2,~b=5\\\\ \overline{1ab}=160=2^4\times 5,~~a=6,~b=0\\\\[/tex]