title: Binary Floats Represented as Decimal Numbers
body: <p>Not all decimal numbers can be represented exactly using binary floats.</p>
  
  <p><a href="http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html" rel="nofollow">http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html</a></p>
  
  <blockquote>
    <p>There are two reasons why a real number might not be exactly
    representable as a floating-point number. The most common situation is
    illustrated by the decimal number 0.1. Although it has a finite
    decimal representation, in binary it has an infinite repeating
    representation.</p>
  </blockquote>
  
  <p>What about the other way around? Can every single <em>IEEE 754</em> float be represented exactly using a decimal number, if enough digits are used?</p>