Question

1) de a fraçao geratriz das dizimas periodicas simples:

0,242424...
0,123123...

2) de a fraçao geratriz das dizimas periodicas compostas:

2,555...
4,181818...
0,3777...
08131313...
7,1444...
9,234545...

Answer 1

$1) \\ 0,2424...= \frac{24}{99} = \frac{24:3}{99:3} = \frac{8}{33} \\ \\ 0,123123...= \frac{123}{999} = \frac{123:3}{999:3} = \frac{41}{333} \\ ----------------- \\ 2) \\ 2,555...= \frac{25-2}{9} = \frac{23}{9} \\ \\ 4,181818...= \frac{418-4}{99} = \frac{414:9}{99:9} = \frac{46}{11} \\ \\ 0,3777...= \frac{37-3}{90} = \frac{34:2}{90:2} = \frac{17}{45} \\ \\ 0,8131313...= \frac{813-8}{990} = \frac{805:5}{990:5} = \frac{161}{198}$ 

$7,141414...= \frac{714-71}{90} = \frac{643}{90} \\ \\ 9,23454545...= \frac{92345-923}{9900} = \frac{91422:9}{9900:9} = \frac{10158:2}{1100:2} = \frac{5079}{550}$