danielhivrenko
danielhivrenko danielhivrenko
  • 11-09-2019
  • Mathematics
contestada

Convert 5.764764764... to a rational expression in the form of a over b where b ≠ 0.

Respuesta :

gmany
gmany gmany
  • 11-09-2019

Answer:

[tex]\large\boxed{5.764764764...=\dfrac{5,759}{999}}[/tex]

Step-by-step explanation:

[tex]\text{Let}\\\\x=5.764764764...\qquad\text{multiply both sides by 1,000}\\\\1,000x=5,764.764764764...\qquad\text{make the difference}\ 1,000x-x:\\\\1,000x-x=5,764.764764764...-5.764764764...\qquad\text{cancel}\ (\overline{764})\\\\999x=5,759\qquad\text{divide both sides by 999}\\\\x=\dfrac{5,759}{999}[/tex]

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