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April 19, 2015

Posted by **blondie** on Wednesday, December 5, 2007 at 1:45am.

1/2

1/3

1/4

1/5

1/6

1/7

1/8

1/9

1/10

1/11

1/12

State a general rule describing which fractions have decimal forms that terminate and which have decimal forms that repeat.

Now test your rule on at least three new fractions. That is, be able to predict whether a fraction such as or has a terminating decimal or a repeating decimal. Then confirm your prediction.

- Math 115 -
**drwls**, Wednesday, December 5, 2007 at 2:08amYou posted this questin twice.

- Math 115 -
**Cindy**, Tuesday, June 17, 2008 at 9:06pm1/2=0.5

1/3=0.333333333333333

1/4=0.25

1/5=0.2

1/6=0.166666666666667

1/7=0.142857142857143

1/8=0.125

1/9=0.111111111111111

1/10=0.1

1/11=0.090909090909091

1/12=0.083333333333333

- Math 115 -
**Cindy**, Tuesday, June 17, 2008 at 9:09pm1/2=0.5

1/3=0.333333333333333

1/4=0.25

1/5=0.2

1/6=0.166666666666667

1/7=0.142857142857143

1/8=0.125

1/9=0.111111111111111

1/10=0.1

1/11=0.090909090909091

1/12=0.083333333333333

fractions with denominators of 3,6,7,9,11,12 (or multiples of these numbers) have decimal forms that repeat, while fractions with denominators of 2,4,5,8,10 (or multiples of these numbers)have decimal forms that terminate.

i predict that 1/25 has a terminating decimal

reason: 25 is a multiple of 5, which has a terminating decimal

1/25=.04 correct

Any power of 10 only has 2 and 5 as prime factors. So if the reduced fraction has a denominator with factors other than 2 or 5, those factors will always be there, and there will be no way to get the fraction expressed with a power of 10 for the denominator. So in conclusion: if the reduced form of the fraction has only 2 and 5 for prime factors in its denominator, then the decimal terminates.

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