Question

como escrever na forma de fração as seguintes Dizima Periodicas
A)-0,888
B)0,3737
C)-1,2121
D)0,0505

Answer 1

A) $x=-0,888...=-0,\overline{8}$

$10x=-8,888...=-8,\overline{8}\\ \\ \\ 10x-x=-8,888...-\left(-0,888... \right )\\ \\ 9x=-8,888...+0,888...\\ \\ 9x=-8,\overline{8}+0,\overline{8}\\ \\ 9x=-8\\ \\ \boxed{x=-\dfrac{8}{9}}$


B) $x=0,3737...=0,\overline{37}$

$100x=37,3737...=37,\overline{37}\\ \\ \\ 100x-x=37,3737...-0,3737...\\ \\ 99x=37,\overline{37}-0,\overline{37}\\ \\ 99x=37\\ \\ \boxed{x=\dfrac{37}{99}}$


C) $x=1,2121...=1,\overline{21}$

$100x=121,2121...=121,\overline{21}\\ \\ \\ 100x-x=121,2121...-1,2121...\\ \\ 99x=121,\overline{21}-1,\overline{21}\\ \\ 99x=120\\ \\ x=\dfrac{120}{99}\\ \\ \boxed{x=\dfrac{40}{33}}$


D) $x=0,0505...=0,\overline{05}$

$100x=5,0505...=5,\overline{05}\\ \\ \\ 100x-x=5,0505...-0,0505...\\ \\ 99x=5,\overline{05}-0,\overline{05}\\ \\ 99x=5\\ \\ \boxed{x=\dfrac{5}{99}}$