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

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

 

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

 

 

 

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