non terminating decimals are produced in cases of division by prime numbers except by 2 and 5.
options a and c are effectively the same because they have the same nonterminating prime in their denominator ie 3. 15 = 5*3 and 5 is terminating. so both would yeild the same M. therefore, none of them is the correct option.
now 4/9 gives M=1 which incidentally is also M for option a ie 1/3. so option e is out.
now 1/11 gives M = 2 whereas 2/7 gives M=6 which is the biggest. 2/7=0.285714
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I am the master of my fate :
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