how do i convert 7.4285714285714 to a fraction

Guest Aug 29, 2017

what ever equation you put in to get that number just put it in here


im sure they can give you a better number to work with

Atroshus  Aug 29, 2017

Here's a method to convert any repeating decimal to a fraction. 


The first step is to set it equal to a variable; I'll use the standard one, x.




Next step is to get only one portion of the repeating portion to the right hand side of the equation. I will demonstrate this:


\(7.428571428571...=x\) Continue moving the decimal point to the right until you make it to the start of the repeating portion again.
\(7428571.428571...=1000000x\) Of course, if you move the decimal place, it the the same as multiplying by 10. We must keep this equation balanced. 


\(\begin{align} 742857.428571&=100000x\\ 7.42857142857...&=x\\ \end{align}\)


Subtract the equations together to get the following:




Divide by the coefficient of x on both sides.




This is your final answer. I do not believe the numerator and denominator have any common factors. 

TheXSquaredFactor  Aug 29, 2017

Well, remember when I said that it has no common factors? Well, I was wrong. 


It turns out that the GCF of  7428564 and 999999 is not 1. 


It turns out that the GCF of both of those numbers is 142857. Wow!


Therefore, \(\frac{7428564}{999999}\div\frac{142857}{142857}=\frac{52}{7}=7\frac{3}{7}\)


That looks so much nicer. I think you'd agree!

TheXSquaredFactor  Aug 29, 2017

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