I WILL GIVE BRAINLIEST PLEASE HELP (picture)

Mathematics

1 answer:

Blizzard [7]3 years ago

8 0

$0.\overline{7}=0.777...\\\\x=0.777...\qquad\text{multiply both sides by 10}\\\\10x=7.777...\\\\\text{Make the difference}\\\\10x-x=7.777...-0.777...\\\\9x=7\qquad\text{divide both sides by 9}\\\\x=\dfrac{7}{9}\\\\Answer:\ \boxed{0.\overline{7}=\dfrac{7}{9}}\\-----------------\\You\ can\ remember\\\\\dfrac{1}{9}=0.\overline{1}\\\\\dfrac{2}{9}=0.\overline{2}\\\\\dfrac{3}{9}=0.\overline{3}\\\\\dfrac{4}{9}=0.\overline{4}\\\vdots\\\\\dfrac{8}{9}=0.\overline{8}$

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