Write 0.319319... as a fraction in its lowest terms

x = 0.319319... As there are three numbers that are recurring, we multiply x by 1000. 1000x = 319.319319... Then we can remove the recurring part by subtracting x from 1000x. 999x = 319 x = 319/999. We note that gcd(319,999) = 1, where gcd is the greatest common denominator, so 319/999 is a fraction in its lowest term.