Question

The number of zeros between decimal & first significant digit in${\left(\begin{array}{c}\frac{1}{6}\end{array}\right)}^{200}$ are

Answer 1

Let $N={\left(\frac{1}{6}\right)}^{200}$
Taking log both side on base 10.
$\log N=200\log \frac{1}{6}=-200\log 6=-200(\log 2+\log 3)=-200(.301+.477)=155.6$
Hence, number of required cyphers $=155$