Question

Gente, eu quero corrigir essas questões mas não sei a resposta correta... podem me ajudar ?!

1. Encontrar a fração geratriz:
a) 3,42222...
b) 0,241212...

2. Resolva as questões:
a) (0,555... + Raiz quadrada de 0,444...) + Raiz quadrada de 0,111...
b) ( Raiz cúbica de 0,343 + 0,13) dividido por 10/0,0222...

Answer 1

1)

$\mathsf{x=3,4222...\times100}\\\mathsf{100x=342,222...\times10}\\\mathsf{1000x=3422,222...}$

$-\underline{\begin{cases}1000x=3422,222...\\100x=342,222...\end{cases}}$

$\mathsf{900x=3080\rightarrow\,x=\dfrac{3080}{900}=\dfrac{154}{45}}$

b)

$\mathsf{y=0,24121212...\times100}\\\mathsf{100y=24,121212...\times100}\\\mathsf{10000y=2412,121212....}$

$-\underline{\begin{cases}10000y=2412,121212...\\100y=24,121212...\end{cases}}$

$\mathsf{9900y=2388\rightarrow\,y=\dfrac{2388}{9900}=\dfrac{199}{825}}$

2)

a)

$\mathsf{0,555...+\sqrt{0,444...}+\sqrt{0,111...}}$

$\mathsf{\dfrac{5}{9}+\sqrt{\dfrac{4}{9}}+\dfrac{1}{9}}$

$\mathsf{\dfrac{5}{9}+\dfrac{2}{3}+\dfrac{1}{9}}$

$\mathsf{\dfrac{5+6+1}{9}=\dfrac{12}{9}=\dfrac{4}{3}}$

b)

$\mathsf{\dfrac{\sqrt[3]{0,343}+0,13}{\dfrac{10}{0,0222...}}}$

$\mathsf{\dfrac{0,7+0,13}{\dfrac{10}{\dfrac{1}{45}}}}$

$\mathsf{\dfrac{0,83}{10.45}}}$

$\mathsf{\dfrac{0,83}{450}}\\\mathsf{\dfrac{\dfrac{83}{100}}{450}}$

$\mathsf{\dfrac{83}{100}.\dfrac{1}{450}=\dfrac{83}{45000}}$