Express $0.10101_2$ as a base 10 fraction in reduced form.

$$\\0.1_2=\frac{1}{2}\\\\ 0.001_2=\frac{1}{2^3}=\frac{1}{8}\\\\ 0.00001_2=\frac{1}{2^5}=\frac{1}{32}\\\\ so\\\\ 0.10101_2=\frac{1}{2}+\frac{1}{8}+\frac{1}{32}\\\\$$

$${\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{32}}}} = {\frac{{\mathtt{21}}}{{\mathtt{32}}}} = {\mathtt{0.656\: \!25}}$$