Q&A #7093

Teachers' Lounge Discussion: Converting repeating decimals to fractions

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From: Loyd

To: Teacher2Teacher Public Discussion
Date: 2003011710:42:06
Subject: Re: Teaching repeating decimals to 7th graders

To understand repeating decimals, I would think they need to
understand that fractions mean divide the numerator by the denominator
and that often the resulting decimal repeats.  Let the student work
examples on their calculators and if you have computers available let
them practice with that.  

You might try letting them do homework at home on computers if they
have one.  For example on Excel by formatting cells as fractions in
column A and column B as numbers with 15 decimal places, you can see
the repeating patterns on those that repeat.  1/6 is rounded up in the
last decimal place and others may be also. 

   1/4  	0.250000000000000
   1/5  	0.200000000000000
   1/6  	0.166666666666667
   1/7  	0.142857142857143
   1/13 	0.076923076923077
   1/17 	0.058823529411765
   1/9  	0.111111111111111
   2/9  	0.222222222222222
   1/3  	0.333333333333333
   1/6  	0.166666666666667
Another thing a student should know is that a fraction will repeat at
the most 1 less than the size of the denominator.  For example, 1/7
repeats after 6 places and so does 1/13.  I think 1/17 repeats in 16
places, but the above doesn't show that many places.  

The students need to have an understanding of infinity since when they
subtract, they need to think of a decimal string that doesn't end, but
when you subtract the result is zero were the minuend and subtrahend
digits are the same. (see my previous post).

Lastly, I am amazed that 7th graders worry about this type of problem.
I didn't see these problems until graduate school.  They fascinated me
when I first learned them.  The next time I saw them was in a ninth
grade algebra book (used nowadays by some 7th graders).  That is the
way it is now, we are moving more and more material into the lower
grades.  That is OK, but students at that age may or may not
appreciate these problems.  

As extra credit, you might let them divide 1 by 17 to find the
repeating part.  

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