Final answer:
.42857142857 as a fraction is 3/7. This is found by setting the decimal equal to x, multiplying the equation by 10^6, subtracting the original equation, and then simplifying the resulting fraction by dividing both the numerator and denominator by their greatest common divisor, which is 7.
Step-by-step explanation:
The number .42857142857 is a repeating decimal, which means it's a fraction in disguise. To convert it into a fraction, let's call this number x:
x = 0.42857142857...
Multiplying both sides of this equation by 10^6 (because the repeating part is 6 digits long) will give us:
1000000x = 428571.428571...
Now let's subtract the original equation (x = 0.42857142857...) from this new equation to get rid of the decimal:
1000000x - x = 428571.428571... - 0.42857142857...
999999x = 428571
Now we divide both sides by 999999 to find x:
x = 428571 / 999999
The fraction 428571 / 999999 can be simplified by dividing both numerator and denominator by the greatest common divisor. In this case, the greatest common divisor is 7, so when we divide both by 7, we get:
x = 3 / 7
Therefore, 0.42857142857 as a fraction is 3/7.