BigDecimal from Double incorrect value?

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When you create a double, the value 0.3 cannot be represented exactly. You can create a BigDecimal from a string without the intermediate double, as in

new BigDecimal("0.3")

A floating point number is represented as a binary fraction and an exponent. Therefore there are some number that cannot be represented exactly. There is an analogous problem in base 10 with numbers like 1/3, which is 0.333333333….. Any decimal representation of 1/3 is inexact. This happens to a DIFFERENT set of fractions in binary, and 0.3 is one of the set that is inexact in binary.

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