Repeating decimal help

• Sep 26th 2009, 09:12 PM
Math Noob
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?
• Sep 26th 2009, 09:20 PM
Chris L T521
Quote:

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 $\displaystyle x=.208\overline{3}$.

So it follows that $\displaystyle 1000x=208.\overline{3}$ and $\displaystyle 10000x=2083.\overline{3}$. Now what is $\displaystyle 10000x-1000x$ 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. :)
• Sep 26th 2009, 09:42 PM
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 (Lipssealed)
• Sep 27th 2009, 03:39 AM
mr fantastic
Quote:

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 (Lipssealed)

• Sep 28th 2009, 01:16 AM
Math Noob
• Sep 28th 2009, 03:12 AM
aidan
Quote:

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

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

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

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

which is also this

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

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

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