Question

Encontre a geratriz das dízimas a seguir, apresentando-as na forma de uma fração irredutível

a)3,7777...=


b) 2,51=


c) 1,488888888..=


d) 2,13444444444...=

Answer 1

$a)3,777...=3+ \frac{7}{9}= \frac{27+7}{9}= \frac{34}{9}\\\\b) 2,51= \frac{251}{100}\\\\c)1,4888...=1+ \frac{48-4}{90}=1+ \frac{44}{90}= \frac{90+44}{90}= \frac{134}{90}= \frac{67}{45}\\\\d)2,13444...=2+ \frac{134-13}{900}=2+ \frac{121}{900}= \frac{1800+121}{900}= \frac{1921}{900}$

Answer 2

a)3,77...= 3 + 7/9 = 34/9


b) 2,51= 251/100 


c) 1,4888...= 1 + (48-4)/90 = 1+ 44/90 = 134/90 = 67/45


d) 2,13444...= 2 + (134-13)900 = 2+ 121/900 = 1921/900