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# how to convert fractions

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how do i convert 7.4285714285714 to a fraction

Guest Aug 29, 2017
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#1
+38
0

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
#2
+1119
+1

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.

$$7.428571428571...=x$$

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:

$$7428564=999999x$$

Divide by the coefficient of x on both sides.

$$x=\frac{7428564}{999999}$$

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

TheXSquaredFactor  Aug 29, 2017
#3
+1119
+1

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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