Question

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

Answer 1

let x = the repeating decimal part only, a.k.a x = 0.764764...

since there are three repeating digits, let's try multiplying x by 1000 (three zeroes)

1000x = 764.764764... etc.

if we subtract 1000x - x we get
764.764764... - 0.764764... we get just 764 (the decimal part crosses out)

so 999x = 764
dividing both sides by 999 will get you x in a fraction form. in other words, we've converted x to a fraction.

now, since it's 5.764.. and not just 0.764, add on 5 to your x value

then convert the result back into an improper fraction