Question

como faço para encontrar a fraçao geratriz das dizimas periodicas:
2,0909....
3,151515...
6,0666.....
0,5727272....

Answer 1

$2,0909...=2+ \frac{9}{99} = \frac{207}{99}= \frac{69}{33}= \frac{23}{11}$

$3,1515...=3+ \frac{15}{99}= \frac{312}{99}= \frac{104}{33}$

$6,0666...=6+ \frac{6}{90}= \frac{546}{90}= \frac{273}{45}= \frac{91}{15}$

$0,57272...= \frac{572-5}{990}= \frac{567}{990}= \frac{189}{330}= \frac{63}{110}$

Answer 2

2 +9/99 = 207/99 = 69/33 = 23/11

3+15/9 = 312/99 = 104/33

6 +6/90 = 546/90 = 273/45 = 91/15

572-5/990 = 567/990 = 189/330 = 63/110