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3 years ago

Convert into fraction: 0.612 the 12 reapeating forever plz help

Mathematics

2 answers:

Charra [1.4K]3 years ago

4 0

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

Mars2501 [29]3 years ago

3 0

Answer:

$\large\boxed{0.6\overline{12}=\dfrac{101}{165}}$

Step-by-step explanation:

$x=0.612121212...\qquad\text{multiply both sides by 10}\\\\(1)\qquad10x=6.12121212...\qquad\text{multiply both sides by 100}\\\\(2)\qquad1000x=612.12121212...\qquad\text{subtract (1) from (2)}\\\\1000x-10x=612.12121212...-6.12121212...\\\\990x=606\qquad\text{divide both sides by 990}\\\\x=\dfrac{606}{990}\qquad\text{simplify}\\\\x=\dfrac{606:6}{990:6}\\\\x=\dfrac{101}{165}$

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