Question

Determine a fração geratriz de cada número decimal abaixo : A) 0,525252...) R= B) 0,666...)R= C) 0,32444...R= D) 5,241241241...R= E) 0,48121121121...R= F) 34,212121...R= G) 5,131131131...R= H) 0,643777...R= ​

Answer 1

Explicação passo-a-passo:

a)

$\sf 0,525252\dots=\red{\dfrac{52}{99}}$

b)

$\sf 0,666\dots=\dfrac{6}{9}=\dfrac{6\div3}{9\div3}=\red{\dfrac{2}{3}}$

c)

$\sf 0,32444\dots=\dfrac{324-32}{900}=\dfrac{292}{900}=\red{\dfrac{73}{225}}$

d)

$\sf 5,241241\dots=\dfrac{5241-5}{999}=\red{\dfrac{5236}{999}}$

e)

$\sf 0,48121121\dots=\dfrac{481121-48}{99900}=\red{\dfrac{48073}{99900}}$

f)

$\sf 34,2121\dots=\dfrac{3421-34}{99}=\dfrac{3387}{99}=\red{\dfrac{1129}{33}}$

g)

$\sf 5,131131\dots=\dfrac{5131-5}{999}=\red{\dfrac{5126}{999}}$

h)

$\sf 0,643777\dots=\dfrac{6437-643}{9000}=\dfrac{5794}{9000}=\red{\dfrac{2897}{4500}}$