Find the smallest positive rational number by which 1/7 should be multiplied so that its decimal expansion terminates after 2 places of decimal.
We know when our denominator in form of 2n5m , than we get terminating decimal digit , And it depends on the value of m or n , if we have m > n than decimal digits terminates after m or if we have n > m than decimal digits terminates after n .
And here we have , So our numerator must be 7 , so we can cancel out 7 from denominator to get terminating decimal digits ,
As we know 5 > 2 , And 52 > 22 ,S o to place 52 in denominator we get smaller rational number in comparison to place 22 .
Our smallest rational number by which should be multiplied so that its decimal expansion terminates after 2 places of decimal. = ( Ans )