The Popular Vote is not what actually elects our President. The President is elected through a process we call the Electoral College.
Here are the top 10 closest Presidential Elections (after the 1800 Presidential Election) by the difference in the Electoral College Vote totals (listed by Electoral College Vote Difference {Presidents total votes vs. total vote of all the other candidates running in that election}, Election Year, Elected President):
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-93 – Election of 1824 – John Quincy Adams
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1 – Election of 1876 – Rutherford B. Hayes
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5 – Election of 2000 – George W. Bush
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23 – Election of 1916 – Woodrow Wilson
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35 – Election of 2004 – George W. Bush
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36 – Election of 1848 – Zachary Taylor
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37 – Election of 1884 – Grover Cleveland
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39 – Election 1812 – James Madison
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46 – Election of 1836 – Martin Van Buren
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52 – Election of 1856 – James Buchanan