SOLUTION: e.g. 0.1111... = 1/9 So then how would I convert 0.0238095238095238095... (238095 is a recurring decimal)to a fraction? Thank you!

Question 503505: e.g. 0.1111... = 1/9
So then how would I convert 0.0238095238095238095... (238095 is a recurring decimal)to a fraction?
Thank you!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
convert 0.0238095238095238095... (238095 is a recurring decimal)to a fraction?
----
Let x = 0.0238095238095238095...
Then 10x = 0.238095238095...
And 10^7x = 238095.238095238095
------------------------------
Subtract the 2nd line from the 3rd to get:
(10^7-10)x = 238095
---
x = 238095/[10000000-10] = 238095/9,999,990
=============================================
Cheers,
Stan H.
RELATED QUESTIONS
how Convert the recurring decimal 2.417417 to a fraction. You must use algebra. (answered by ewatrrr)

How do you convert the recurring decimal 0.23333333 to a fraction. Give your answer in... (answered by khwang,Robee16,Alan3354,greenestamps)

Infinite geometric series. The question asks me to write the repeating decimal .999...... (answered by stanbon)

Hi,my name is Natalia. I solved two problems, but I'm not sure that I did it right. I... (answered by venugopalramana)

Repeating decimals(multiplication and division) (a.) 0.888...divided by 2/9 (b.)... (answered by CubeyThePenguin)

How do i convert a decimal to a... (answered by elima)

Hi can you please show how to express this recurring decimal as a fraction... (answered by Edwin McCravy)

Convert the fallowing expression a^(1/ln a) using base e, for a > 0 and a≠1. So i... (answered by Edwin McCravy)

0.72r (just the 2 recurring) as a fraction. Can you show the workings out so i can see... (answered by stanbon,Alan3354,MathTherapy)