If A = 0.abcabc _____, then by what number A should be multiplied so as to get an integeral value?
Both 2997 and 1998
For \(A=0.\overline{abc}\), the standard conversion gives \(A=\dfrac{abc}{999}\). The multiplier must be a multiple of 999 to clear the denominator for every choice of \(abc\).
Among the options: \(1998=2\times 999\) and \(2997=3\times 999\); 1000 is not a multiple of 999. Hence both 2997 and 1998 work.
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