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$\ \phantom{=\quad}\dfrac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}\\~\\ =\quad\dfrac{10^{2000}(1+10^{2})}{10^{2000}(10+10)}\\~\\ =\quad\dfrac{(1+10^{2})}{(10+10)}\\~\\ =\quad\dfrac{(1+100)}{20}\\~\\ =\quad\dfrac{1}{20}+\dfrac{100}{20}\\~\\ =\quad\dfrac{1}{20}+5$

The whole number closest to  5  and  1/20th  is  5 .