1) 0,666... = 2/3

2) 0,333... = 1/3

3) 0,222... = 2/9

4) 0,121212... = 1/8

5) 0,151515... = 1/6

6) 2,343434...​ = 232/99

Verified answer

Resposta:

Eis as frações correspondentes às dízimas apresentadas:

• 0,666...: 2/3
• 0,333...: 1/3
• 0,222...: 2/9
• 0,121212...: 4/33
• 0,151515...: 5/33
• 2,343434...: 232/99

Explicação passo a passo:

Vamos determinar as frações equivalentes às dízimas periódicas dadas:

• 0,666...:

[tex]0,666...=x\\10\times0,666...=10\times x\\6,666...=10x\\\\6,666...=10x\\(-)\\0,666...=x\\(=)\\6=9x\\\frac{6}{9}=x\\\frac{6\div3}{9\div3}=x\\\frac{2}{3}=x\\\\Logo:\\0,666...=\frac{2}{3}[/tex]

• 0,333...:

[tex]0,333...=x\\10\times0,333...=10\times x\\3,333...=10x\\\\3,333...=10x\\(-)\\0,333...=x\\(=)\\3=9x\\\frac{3}{9}=x\\\frac{3\div3}{9\div3}=x\\\frac{1}{3}=x\\\\Logo:\\0,333...=\frac{1}{3}[/tex]

• 0,222...:

[tex]0,222...=x\\10\times0,222...=10\times x\\2,222...=10x\\\\2,222...=10x\\(-)\\0,222...=x\\(=)\\2=9x\\\frac{2}{9}=x\\\\Logo:\\0,222...=\frac{2}{9}[/tex]

• 0,121212...:

[tex]0,121212...=x\\100\times0,121212...=100\times x\\12,121212...=100x\\\\12,121212...=100x\\(-)\\0,121212...=x\\(=)\\12=99x\\\frac{12}{99}=x\\\frac{12\div3}{99\div3}=x\\\frac{4}{33}=x\\\\Logo:\\0,121212...=\frac{4}{33}[/tex]

• 0,151515...:

[tex]0,151515...=x\\100\times0,151515...=100\times x\\15,151515...=100x\\\\15,151515...=100x\\(-)\\0,151515...=x\\(=)\\15=99x\\\frac{15}{99}=x\\\frac{15\div3}{99\div3}=x\\\frac{5}{33}=x\\\\Logo:\\0,151515...=\frac{5}{33}[/tex]

• 2,343434...:

[tex]2,343434...=x\\100\times2,343434...=100\times x\\234,343434...=100x\\\\234,343434...=100x\\(-)\\2,343434...=x\\(=)\\232=99x\\\frac{232}{99}=x\\\\Logo:\\2,343434...=\frac{232}{99}[/tex]