# Thread: Converting recurring decimals to a mixed number using algebra?

1. ## Converting recurring decimals to a mixed number using algebra?

Hi guys this was a question which I was stuck on and I was wondering if anyone could give me some guidance.

1) Convert the recurring decimal 2.136 (the 3 and the 6 are the only digits that recur sorry for not using the correct notation, I don't know how to get it online) to a mixed number.

Thanks for any help and advice.

2. ## Re: Converting recurring decimals to a mixed number using algebra?

Originally Posted by MattA147
Hi guys this was a question which I was stuck on and I was wondering if anyone could give me some guidance.
1) Convert the recurring decimal 2.136 (the 3 and the 6 are the only digits that recur sorry for not using the correct notation, I don't know how to get it online) to a mixed number.

If $\displaystyle S=2.1\overline{36}$ then $\displaystyle 10S=21.\overline{36}~\&~1000S=2136.\overline{36}$

What does $\displaystyle 1000S-10S=~?$

3. ## Re: Converting recurring decimals to a mixed number using algebra?

Thanks for your post but I still don't quite understand...

4. ## Re: Converting recurring decimals to a mixed number using algebra?

Originally Posted by MattA147
Thanks for your post but I still don't quite understand...
What is there to not understand?

You now have two numbers with the same decimal part. Subtract them,

What do you get?

5. ## Re: Converting recurring decimals to a mixed number using algebra?

2126? Do the decimal parts cancel?

6. ## Re: Converting recurring decimals to a mixed number using algebra?

Originally Posted by MattA147
2126? Do the decimal parts cancel?
Not quite, it is $\displaystyle 1000S-10S=2115$. Thus $\displaystyle 990S=2115$. Solve for $\displaystyle S$, in fraction form.

$\displaystyle S$ was the original number.

7. ## Re: Converting recurring decimals to a mixed number using algebra?

This makes sense now thanks very much. Have a good evening.