Question

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

Answer 1

`\large\boxed{5.764764764...=(5,759)/(999)}`

Explanation:

`\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=(5,759)/(999)`