Question

Determine a fração geratriz de cada dízima periódica

a) 2,555... =

b) 4,75 =

c) 2,278278... =

por favor é pra amanhã​

Answer 1

Resposta:

a) 2,555... =(25-2)/9=23/9

b) 4,75... = (475-4)/99=471/99

c) 2,278278... = (2278-2)/999=2276/999

Answer 2

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$\boxed{\begin{array}{l}\tt a)~\sf x=2,555..\cdot10\\\sf 10x=25,555...\\-\underline{\begin{cases}\sf 10x=25,555....\\\sf x=2,555....\end{cases}}\\\sf 9x=23\\\sf x=\dfrac{23}{9}\\\tt b)~\sf y=4,757575....\cdot100\\\sf 100y=475,757575...\cdot100\\\sf 10000y=47575,757575....\\-\underline{\begin{cases}\sf 10000y=47575,757575...\\\sf 100y=475,757575....\end{cases}}\\\sf 9900y=47100\\\sf y=\dfrac{47100\div300}{9900\div300}\\\sf y=\dfrac{157}{33}\end{array}}$

$\boxed{\begin{array}{l}\tt c)~\sf z=2,278278...\cdot1000\\\sf 1000z=2278,278278...\cdot1000\\\sf 1000000z=2278278,278278...\\-\underline{\begin{cases}\sf1000000z=2278278,278278...\\\sf 1000z=2278,278278...\end{cases}}\\\sf999000z=2276000\\\sf z=\dfrac{2276000\div1000}{999000\div1000}\\\sf z=\dfrac{2276}{999}\end{array}}$