skumar Posted May 1, 2005 Share Posted May 1, 2005 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. Quote Link to comment Share on other sites More sharing options...
skumar Posted May 1, 2005 Author Share Posted May 1, 2005 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. Quote Link to comment Share on other sites More sharing options...
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