Question

As frações geratrizes das dízimas 0,3333....... e 0,252525 ..... são respectivamente:

2/9 e 5/9

1/3 e 25/99

3/9 e 25/99

1/3 e 25/9

3/9 e 2/99​

Answer 1

Resposta:

$\blue{0,333... }= \dfrac{3 \div 3}{9 \div 3} = \blue{\dfrac{1}{3} }\\ \\ ou \\ \\x = 0,3333...\\ \\x = 0,333...×10\\ \\10x = 3,333...\\ \\ 10x - x = 3,333... - 0,333...\\ \\ 9x = 3\\ \\x = \dfrac{3÷3}{9÷3}\\ \\\orange{x = \dfrac{1}{3}}\\ \\ x = 0,2525...\\ \\ x=0,252525... ×10\\ \\10x = 2,525... ×10\\\\ 100x = 25,25 \\ \\100x - x = 25,25... - 0,225...\\ \\ 99x = 25\\ \\ \orange{x = \dfrac{25}{99}}$

$\green{Letra \:b) \:\dfrac{1}{3} \:e \:\dfrac{25}{99}}$

Bons Estudos!