Question

QUAL É O VALOR,EM FORMA DE FRAÇÃO IRREDUTIVEL, DA EXPRESSÃO 
¯¯\/ 0,111...- 2,888..+1,7333...

Answer 1

Olá, Rayclemente.

$\sqrt{0,111..}.- 2,888..+1,7333...=\\\\ =\sqrt{\frac19}-(2+0,888...)+1,7+0,0333...=\\\\ =\frac13-(2+\frac89)+\frac{17}{10}+\frac{0,333...}{10}=\\\\ =\frac13-\frac{18+8}9+\frac{17}{10}+\frac{3}{9\cdot10}=\\\\ =\frac13-\frac{26}9+\frac{17}{10}+\frac1{30}=\\\\ =\frac{30-260+153+3}{90}=\\\\ =-\frac{74}{90}=\\\\ =\boxed{-\frac{37}{45}}$