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Q&A #7093

Teachers' Lounge Discussion: Converting repeating decimals to fractions

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From: Loyd <Loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2004032608:12:28
Subject: Re: Mathematics Teaching; repeating decimals

On 2004032603:00:19, G.S.LAWANIA wrote:
>	
>Please tell me the way of multiplying & dividing recurring decimal
>numbers.
>Thanks
>
1.36363636363636...  =1 4/11 See my post of 4 sep 02

1.58333333333333 = 1 77/132= 1 7/12    See my post of  2 Nov 03

Suppose the problem was to divide 1.58333333333333 by 1.36363636363636
where both numbers are repeating or recurring as you said.  

One could use the long division method but this would be quite
involved.  The answer wouldn't be exact, but it is good enough for
most all applications.  Using a 10 digit calculator, you would get:

1.583333333
-----------
1.363636364

=1.161111109

Then, divide 
1 7/12
---------  = 1 29/180 = 1.161111111111111 repeating
1 4/11

So, the only way I know to express the answer as an exact answer is to
use mixed numbers as in the above problem.  When you convert to a
decimal fraction, the number is repeating.

So, using a calculator to divide a decimal repeating number by another
repeating decimal we got 1.161111109 whereas using the improper
fraction method, we got 1.161111111111111 repeating.  For practical
applications the difference between those two answers is
insignificant.  
Of course, 1 29/180 is exact.

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