Question

Convert 5.764764764 ... to a rational expression in the form of a over b , where b ≠ 0. (4 points)

a
5 and 764 over 999

b
5764 over 9999

c
5 and 764 over 99

d
5 and 999 over 764

Answer 1

5.764764764

let's let x = 0.764764764... (the repeating part only)

therefore, 1000x = 764.764764764...

notice what happens when we subtract

1000x - x = 999x = 764 (the repeating parts from both cancel out)

if 999x = 764, then we can divide both sides by 999 to get x = 764/999
so we have now converted the repeating decimal to a fraction.

going back to the original number, it's

5.764764764 = 5 + 764/999