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 2^{n}5^{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 5^{2 }> 2^{2} ,S o to place 5^{2} in denominator we get smaller rational number in comparison to place 2^{2} .

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 )**

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