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recurring and non recurring decimals


skumar

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Can someone tell me any rule which can be applied to find the values of x and y so as the fraction x/y will be recurring or non recurring decimal.

To put in other words, for what values of x,y will a fraction x/y will be a recurring or a non recurring decimal.

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Got some interesting facts. That helps to solve my query..

Some interesting facts about recurring decimals

A denominator containing only 2 or 5 as factors gives us a non-recurring decimal function. For example,

1/2 = 0.5

1/4 = 1/(2*2) = 0.25

1/8 = 1/ (2*2*2) = 0.125

1/5 = 0.2

1/25 = 1/(5*5) = 0.04 and so on

 

Denominators containing only 3, 7, 11 or higher prime numbers as factor and not even a single 2 or 5 given recurring decimals. For example

 

1/3 = 0.3

1/7 = 0.142857

1/9 = 0.1

1/11 = 0.09

1/13 = 0.076923

1/17 = 0.05882352/94117647 and so on

A denominator with factors partly of the first type and party of the second type, give us a mixed, i,e. party recurring and party non-recurring decimal. For example,

 

1/6 = 1/(2*3) = 0.16

1/15 = 1/ (3*5) = 0.06

1/18 = 1/ (2*9) = 0.05

1/22 = 1/ (2*11) = 0.045 and so on.

Denominator containing all digits 9.

It is very easy to find the decimal equivalent of a faction with denominator containing all nines. It is recurring decimal with digits in the numerator. For example,

 

1/9 = 0.1

2/9 = 0.2

5/9 = 0.5

23/99 = 0.23

50/99 = 0.50

112/999 = 0.112 and so on.

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