Q&A #7093

Teachers' Lounge Discussion: Converting repeating decimals to fractions

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From: Loyd

To: Teacher2Teacher Public Discussion
Date: 2004032609:12:28
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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