Note:-
1) Prime numbers in the denominator except 2 and 5 yield repeating decimals, no matter what is the numerator.If the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5, the decimal expression terminates. If there is any prime factor in the denominator other than 2 or 5, then the decimal expression repeats.
2) 1/3 = 0.3333…, 1/7=0.142857142857.., 1/11=0.090909...
3) Multiplying any integer value with 1/3 or 1/7 or 1/11 or 1/(prime number except 2,5) only shifts the decimal point.
4) As long as the fraction is in lowest terms, the numerator doesn’t matter at all.
Let's simplify options:-
A. 17/44=(17/\(2^2\))*1/11 ; 17/4 has no role here. The number of recurring decimals(with different digits) solely depends on the number of recurring decimals of 1/11, that is 2.
B. 5/6=(5/2)*1/3; In line with the above reasoning, #recurring decimals would be 1.
C. 41/66=(41/2)*1/3*1/11; #recurring decimals would be 2. (since the #recurring decimals of 1/11 is 2)
D. 1/120=(1/(\(2^3*5\)))*1/3; #recurring decimals would be 1. (since the #recurring decimals of 1/3 is 1)
E. I don't want to break my head here.It must contain the maximum number of repeating decimals(with different digits) by method of elimination.

Ans. (E)
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Regards,

PKN

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