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How to convert repeating decimal to fraction ?

Posted on 2014-12-14
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Last Modified: 2014-12-14
Please see question in attached file.

We know how to convert most repeating decimals to fraction but in this problem the tenths digit
isn't repeating.  Is that a incorrect question ?   If not, please explain how to do this problem.
repeat.png
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Question by:naseeam
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11 Comments
 
LVL 32

Expert Comment

by:phoffric
ID: 40499442
0.0102 is not repeating.
<EDIT> oh, I didn't see the bar over 102.
never mind
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LVL 1

Author Comment

by:naseeam
ID: 40499443
The problem says 102 is repeating.  The tenths place isn't repeating but hundredths, thousandths, and ten thousandths places are repeating.
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LVL 32

Assisted Solution

by:phoffric
phoffric earned 800 total points
ID: 40499444
x = 0.0102102102102102102102
x = 10000x/10000 = 102.102102102102102102.../10000

x = (102/10000) + 0.102102102102102102...

y = 0.102102102102102102...
and you say you know how to make y a fraction.

x =  (102/10000) + y
and you can add the two fractions together.
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LVL 84

Accepted Solution

by:
ozo earned 1200 total points
ID: 40499445
x= 0.0102102102102...
999*x=x*1000-x=
  10.2102102102102...
   -0.0102102102102...
=10.2
x = 10.2/999 = 102/9990=17/1665
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LVL 84

Expert Comment

by:ozo
ID: 40499454
x =  (102/10000) + y
I think you mean (102+y)/10000)
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LVL 1

Author Comment

by:naseeam
ID: 40499455
Sorry I forgot to mention that this problem is assigned to Fifth Graders.  Is it possible to provide a solution that doesn't require algebra?
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LVL 32

Expert Comment

by:phoffric
ID: 40499458
>> I think you mean (102+y)/10000)
Yes I did, and was correcting my post when I saw your post.
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LVL 84

Expert Comment

by:ozo
ID: 40499462
What solution that doesn't require algebra would a 5th grader give for
   ____
0.102  / 10
?

What if we just wrote 0.0102102102102...  in place of each x ?
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LVL 1

Author Comment

by:naseeam
ID: 40499469
>>  x = 10.2/999 = 102/999=34/333
it's 102/9990
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LVL 84

Expert Comment

by:ozo
ID: 40499474
I guess I was faster correcting my post than phoffric :-)
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LVL 1

Author Closing Comment

by:naseeam
ID: 40499477
Experts replied immediatedly with great solutions.
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