Question

Resolva as dízimas periódicas abaixo, encontrando a fração geratriz
a)1,233333
b)0,878787
c)3,434343
d)5.67878​

Answer 1

$> resolucao \\ \\ \geqslant fracao \: geratriz \\ \\ a > 1.23333.... \\ a > \frac{123 - 12}{90} \\ a > \frac{111 \div 3}{90 \div 3} \\ a > \frac{37}{30} \\ \\ = = = = = = = = = = = = = = = = = = = = = \\ \\ \\ b > 0.878787.... \\ b > \frac{87 \div 3}{99 \div 3} \\ b > \frac{29}{33} \\ \\ = = = = = = = = = = = = = = = = = = = = = \\ \\ \\ c > 3.434343.... \\ c > \frac{343 - 3}{99} \\ c > \frac{340}{99} \\ \\ = = = = = = = = = = = = = = = = = = = = = = \\ \\ d > 5.67878.... \\ d > \frac{5678 - 56}{990} \\ d > \frac{5622 \div 6}{990 \div 6} \\ d > \frac{937}{165} \\ \\ \\ > < > < > < > < > < > < > < >$