Show that only a few multiples of .01 decimal are powers of 2 I am asking this to advance the argument that BigDecimal is better than float or double for representing exact amounts of currency.  

Can someone refer me to a proof that between any two integers there are only four values that multiples of .01 and can be exactly represented in base 2?  Or at least confirm I'm correct in my belief that it's true?
Hint: The four values are $25/100 = 1/4$ and its multiples.

If all you want to do is store an exact amount of currency, you can use an integer which represents the amount of cents. (This is known as fixed-point arithmetic.)