Question

Qual a fração geratriz das dizimas periodicas ?

0,777...
2,111...
32,4545...
2,15555...
25,2344...
721,10333...

Answer 1

   0,777... = 7/9
   
  2,111... = 2  1/9 = 19/9
  
32,4545...= $32 \frac{45}{99} = \frac{3213}{99} = \frac{1071}{33}= \frac{357}{11}$

2,1555... = $2 \frac{15-1}{90} =2 \frac{14}{90} = \frac{194}{90} = \frac{97}{45}$

25,2344...= 25 $\frac{234-23}{900} = 25 \frac{211}{900} = \frac{22711}{900}$

721,1033...=$721 \frac{103-10}{900} = 721 \frac{93}{900}= \frac{648993}{900} = \frac{216331}{300}$




























 

Answer 2

0,777... = 7/9
2,111... = (21-2)/9  = 19/9
32,4545... = (3245-32)/99 =3213/99 = 357/11 
2,1555... = (215 - 21)/ 90 = 194/90 = 97/45
25,23444... = (25234 - 2523)/9 = 22711/9 
721,10333... = (721103 - 72110)/9900 = 648993/900 = 216331/300