Question 174
Find the integer $m$ so that
$$
10^{m} \lt \frac{1}{2} \times \frac{3}{4} \times \frac{5}{6} \times \ldots \frac{99}{100} \lt 10^{m+1}
$$
$$
10^{m} \lt \frac{1}{2} \times \frac{3}{4} \times \frac{5}{6} \times \ldots \frac{99}{100} \lt 10^{m+1}
$$