Which one of the following numbers is a non-terminating and repeating decimal?
311
If pq is a rational number in its standard form (HCF of p and q is 1) whose decimal expansion is terminating, then q=2m×5n
(Decimal expansion of a number is terminating when the denominator is a power of 2 and/or 5, and the H.C.F of the numerator and the denominator is 1)
3924=13×38×3=138
The denominator of 138 is 8 which is 23
Thus, the decimal expansion of 3924 is terminating
4956=7×78×7=78
The denominator of 78 is 8 which is 23
Thus, the decimal expansion of 4956 is terminating
7832=39×216×2=3916
The denominator of 3916 is 16 which is 24
Thus, the decimal expansion of 7832 is terminating
The denominator of 311 is 11 which is 111.
Thus, the decimal expansion of 311 is recurring.