Answer :
To convert a decimal to a fraction, place the decimal number over its place value.
For instance, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction,
[tex]\frac{6}{10}[/tex]Similarly, in 0.42857142857 we have 11 places next to the decimal point. Then, we have
[tex]0.42857142857=\frac{42857142857}{100,000,000,000}[/tex]A fraction is in simplest form when the top and bottom cannot be any smaller, while still being whole numbers. In our case, if we divide by 5 both the numerator and denominador, we obtain
[tex]\frac{42857142857/5}{100,000,000,000/5}=\frac{857142857}{20000000000}[/tex]since 5 is the greatest commun factor, this is the simplified answer.