Question

Encontre a fração geratriz das dízimas periódicas a)0,444. B)0,2777. C)1,3636 d)22,1666

Answer 1

$> resolucao \\ \\ \geqslant fracao \: \: geratriz \\ \\ a > 0.444... \\ a > \frac{4}{9} \\ \\ = = = = = = = = = = = = = = = = = = \\ \\ b > 0.2777... \\ b > \frac{27 - 2}{90} \\ b > \frac{25 \div 5}{90 \div 5} \\ b > \frac{5}{18} \\ \\ = = = = = = = = = = = = = = = = = = \\ \\ c > 1.3636... \\ c > \frac{136 - 1}{99} \\ c > \frac{135 \div 9}{99 \div 9} \\ c > \frac{15}{11} \\ \\ = = = = = = = = = = = = = = = = = = = \\ \\ \\ d > 22.1666..... \\ d > \frac{2216 - 221}{90} \\ d > \frac{1995 \div 3}{90 \div 3} \\ d > \frac{665}{30} \\ \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \geqslant \geqslant$