# Thread: recurring and non recurring decimals

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## recurring and non recurring decimals

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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## Re: recurring and non recurring decimals

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.