MathGroup Archive 1995

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Base 10 to Base 2 conversion error ?

  • To: mathgroup at
  • Subject: [mg1703] Base 10 to Base 2 conversion error ?
  • From: randy_taylor at (Randy Taylor)
  • Date: Mon, 17 Jul 1995 04:04:31 -0400
  • Organization: IDS World Network Internet Access Service, (800)IDS-1680

I hope one of the mathematicians can help me with this one:

Are there any base 10 numbers with two significant digits
to the right of the decimal point that such that conversion
to base 2 and then re-conversion to base 10 does not yield the exact original 
value? I happen to use Intel x86 chips with floating point registers, but
this isn't really a question about the famous Intel floating point problem.

Why do I care? Some people at my company (a maker of retail
store point-of-sale systems) say that no such numbers exist,
and they propose using the floating point format variables
(the C language type double or float) to hold U.S. currency amounts.
I've claimed that the system will not properly keep track of each
penny of we do this. Especially when we divide these amounts by other
floating point amounts. Is this correct? Am I full of hot air?


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