Find the smallest positive rational number by which 1/7 should be multiplied so that its decimal expansion terminates after 2 places of decimal.

Answer :
 

We know when our denominator in form of  2ⁿ5^m  , 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 $\frac{1}{7}$  , So  our numerator must be 7 , so we can cancel out 7 from denominator to get terminating decimal digits  ,
And
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 .
So
Our smallest rational number by which $\frac{1}{7}$  should be multiplied so that its decimal expansion terminates after 2 places of decimal.  = $\frac{7}{5^2} = \frac{7}{25}$                                                          (  Ans  )