1. ## Repeating decimal help

Ok i am stuck in a problem i need some coaching on. This is a repeating decimal, 0.2083 with the last digit 3 repeating i need to form this into a fraction. I don't want the answer but would love to know using the variable x how can i solve this equation?

2. Originally Posted by Math Noob
Ok i am stuck in a problem i need some coaching on. This is a repeating decimal, 0.2083 with the last digit 3 repeating i need to form this into a fraction. I don't want the answer but would love to know using the variable x how can i solve this equation?
Let $x=.208\overline{3}$.

So it follows that $1000x=208.\overline{3}$ and $10000x=2083.\overline{3}$. Now what is $10000x-1000x$ equal to? From there, see if you can solve for x.

You may get a ugly looking fraction, but it simplifies nicely. See how far you can go with this.

3. I would like to see a break down on how and why. Is there a way for you to break this down for me please? I thought when a single digit repeats you only multiply by ten? Then move the decimal towards the right one time then doing the subtracting. I'm confused now lol

4. Originally Posted by Math Noob
I would like to see a break down on how and why. Is there a way for you to break this down for me please? I thought when a single digit repeats you only multiply by ten? Then move the decimal towards the right one time then doing the subtracting. I'm confused now lol

6. Originally Posted by Math Noob
Ok i am stuck in a problem i need some coaching on. This is a repeating decimal, 0.2083 with the last digit 3 repeating i need to form this into a fraction. I don't want the answer but would love to know using the variable x how can i solve this equation?
What was explained above is this:

0.20833333333333333333333333...333

is equivalent to

$\dfrac{2.0833333333333333333333...333}{10}$

& this
$\dfrac{20.833333333333333333333...333}{100}$

& this
$\dfrac{208.3333333333333333333...333}{1000}$

which is also this

$\dfrac{208 + \dfrac{1}{3}}{1000}$
which is also

$\dfrac{ \cfrac{3 \cdot 208 + 1}{3}}{1000}$

and you should be able to reduce that to a simple fraction.