Question

What is 0.42857142857 as a fraction? Express the result in simplest form.

Answer 1

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,

`(6)/(10)`

Similarly, in 0.42857142857 we have 11 places next to the decimal point. Then, we have

`0.42857142857=(42857142857)/(100,000,000,000)`

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

`(42857142857/5)/(100,000,000,000/5)=(857142857)/(20000000000)`

since 5 is the greatest commun factor, this is the simplified answer.