Answer:
Step-by-step explanation:
x=0.6121212... (1)
10x=6.121212... (2)
1000 x=612.121212... (3)
(3)-(2) gives
990 x=606
330x=202
165x=101
x=(101)/165
Answer:
[tex]\large\boxed{0.6\overline{12}=\dfrac{101}{165}}[/tex]
Step-by-step explanation:
[tex]x=0.612121212...\qquad\text{multiply both sides by 10}\\\\(1)\qquad10x=6.12121212...\qquad\text{multiply both sides by 100}\\\\(2)\qquad1000x=612.12121212...\qquad\text{subtract (1) from (2)}\\\\1000x-10x=612.12121212...-6.12121212...\\\\990x=606\qquad\text{divide both sides by 990}\\\\x=\dfrac{606}{990}\qquad\text{simplify}\\\\x=\dfrac{606:6}{990:6}\\\\x=\dfrac{101}{165}[/tex]
