Question

Help Sana identify the smallest natural number that can be multiplied with the fraction $8\frac{1}{15}$ such that the decimal expansion of the resulting fraction is terminating.

Answer 1

$8\frac{1}{15}$ has $15$ in its denominator.

$15=3\times 5$

To make the fraction a terminating decimal, we need to eliminate $3$ in the denominator by multiplying a number that is a multiple of $3.$

Since we are asked for the smallest such natural number, we go with 3 itself.

$8\frac{1}{15}\times 3=\frac{8\times 15+1}{3\times 5}\times 3=\frac{121}{5}$

Now, the denominator is a multiple of $5$. Hence, it will result in a terminating decimal number.

In fact,$\frac{121}{5}=24.2,$ which is a terminating decimal.