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Q.

The smallest rational number by which 1 3   should be multiplied so that its decimal expansion terminates after one place of decimal, is


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a

  3 10  

b

  1 10  

c

  3  

d

3 100   

answer is A.

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Detailed Solution

Given to find the smallest rational number by which 1 3   should be multiplied so that its decimal expansion terminates after one place of decimal.
A rational number is always the product of two rational numbers.
Decimal expansion of a number terminates means the number is rational.
Let x be the least number to be multiplied.
The least possible product is 0.1 = 1 10 .   Therefore the equation becomes,
1 3 x = 1 10 x 3 = 1 10 x = 3 10  
Therefore 3 10   is the smallest rational number by which 1 3   should be multiplied so that its decimal expansion terminates after one place of decimal.  Hence the correct option is 1.
 
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The smallest rational number by which 1 3   should be multiplied so that its decimal expansion terminates after one place of decimal, is