Question

Question 13
Write the denominator of rational number $\frac{257}{5000}$ in the form $2^m\times 5^n$, where m, n are non - negative integers. Hence, write its decimal expansion, without actual division.

Answer 1

Denominator of the rational $\frac{257}{5000}$ number is 5000.
Now, factors of 5000
$=2\times 2\times 2\times 5\times 5\times 5\times 5=(2{)}^3\times (5{)}^4$ which is of the type $2^m\times 5^n$.
Where m = 3 and n = 4 are non - negative integers
$\therefore$ $\frac{257}{5000}=\frac{257}{2^3\times 5^4}\times \frac{2}{2}$
$=\frac{514}{2^4\times 5^4}=\frac{514}{(10{)}^4}$
$=\frac{514}{10000}=0.0514$
Thus, 0.0514 is the required decimal expansion.