Matemática, perguntado por jc9561310gmailcom, 1 ano atrás

determine a fração geratriz de cada uma das dizima periódica
a)0,05222...
b)2,4777...
d)0,1444...​

Soluções para a tarefa

Respondido por GeBEfte
1

a)

0,05222...~=~0,05+0,00222...\\\\\\0,05222...~=~\frac{5}{100}+\frac{2}{900}\\\\\\0,05222...~=~\frac{9~.~5~+~1~.~2}{900}\\\\\\\boxed{0,05222...~=~\frac{47}{900}}

b)

2,4777...~=~2+0,4+0,0777...\\\\\\2,4777...~=~2+\frac{4}{10}+\frac{7}{90}\\\\\\2,4777...~=~\frac{90~.~2~+~9~.~4~+~1~.~7}{90}\\\\\\2,4777...~=~\frac{180+36+7}{90}\\\\\\\boxed{2,4777...~=~\frac{223}{90}}

c)

0,1444...~=~0,1+0,0444...\\\\\\0,1444...~=~\frac{1}{10}+\frac{4}{90}\\\\\\0,1444...~=~\frac{9~.~1~+~1~.~4}{90}\\\\\\0,1444...~=~\frac{9+4}{90}\\\\\\\boxed{0,1444...~=~\frac{13}{90}}

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