Question

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

Answer 1

Answer and Explanation:

To find : The smallest positive rational number by which 1/7 should be multiply so that its decimal expansion terminates after 2 places of decimal ?

Solution :

When the  denominator is in the form of $2^n5^m$ then terminating decimal digit  depends on the value of m or n.

1) If we have m>n, then decimal digit terminates after m

2)  If we have n > m, then digit terminates after n.

We have given, $\frac{1}{7}$

Our numerator must be 7, so we cancel out 7 from the denominator to get terminating decimal digits.

We know 5 > 2, and $5^2 > 2^2$. So, to place $5^2$ in denominator we get a smaller rational number in comparison to place $2^2$.

Our smallest rational number by which $\frac{1}{7}$ should be multiplied, so that its decimal expansion terminates after two places of decimal is given by,

$\frac{7}{5^2}=\frac{7}{25}$