Question

If 241/1000 = 241/2^m5^n find the values of m and n where m and n are non negative integers. Hence write its decimal expansion without actual division

Answer 1

$\frac{241}{1000} = \frac{241}{10 \times 10 \times 10} \\ = \frac{241}{5 \times 2 \times 5 \times 2 \times 5 \times 2} \\ = \frac{241}{ {5}^{3} \times {2}^{3} } \\ \\ i.e. \: m \: = 3 \: and \: \: n = 3$


decimal expansion = 0.241