Is 0.7142857 ... a rational number? why or why not?

The number 0.7142857 is definitely a rational number. This number can also be expressed as 7142857/10000000. Now we know that a rational number is a number that can be expressed as a fraction or a quotient of two integers. The denominator of the fraction can never be equal to zero. In case of the number given we can clearly see that the denominator of this fraction is not zero. The actual fraction of this number is 5/7. In this case we find that the denominator is not zero.