Teacher2Teacher 
Q&A #7093 
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From: Loyd <loydlin@aol.com> To: Teacher2Teacher Public Discussion Date: 2003011709:42:06 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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